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<Text-field style="Annotation Title" layout="Annotation Title"><Font style="Text" size="18">Financial Markets</Font></Text-field>
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<Text-field style="Text" layout="Annotation Title"><Font size="18">Short Interest Rate Models</Font></Text-field>
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<Text-field style="Text" layout="Annotation Title"><Font size="18">Session #16</Font></Text-field>
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<Text-field style="Author" layout="Author">Alejandro Reynoso</Text-field>
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<Text-field style="Heading 1" layout="Heading 1">1. Motivation</Text-field></Title><Presentation-Block>
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<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JSFH</Equation></Text-field>
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<Text-field style="Text" layout="Normal">So far we have looked at static concepts around interest rates and bond and cash flow valuations. There is no meaningful reference to risk, beyod the notions of convexity and duration. It is in the dynamics of rates that we find market risk and all the implications around it.</Text-field>
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<Text-field style="Text" layout="Normal">In the sessions on derivatives these concepts will come back in a richer context related to the mitigation and administration of such risks.</Text-field>
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<Text-field style="Text" layout="Normal">For now, it should suffice to take a look at various models and their implications.</Text-field>
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<Text-field style="Text" layout="Normal">We will talk about short rate processes. These will govern the evolution onf the instantaneous interest rate at any given time. There are two kinds of models.</Text-field>
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<Text-field style="Text" layout="Normal">The so called one factor models, which are the one variable stochastic processes. In this context we can construct then needed curves for valuation at any point in the simulation and thus we can calculate the price of a bond.<Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JSFH</Equation></Text-field>
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<Text-field style="Heading 1" layout="Heading 1">2. Theoretical Framework: Term Structure</Text-field></Title><Presentation-Block>
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<Text-field style="Text" layout="Normal"><Font bold="true">Definitions</Font></Text-field>
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<Text-field style="Text" layout="Normal">In an important paper dated in 1977, Vasicek developed a continuous time model for the term structure of interest rates.</Text-field>
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<Text-field style="Text" layout="Normal">Given certain characteristics of the underlying stochastic process it was possible to reach closed for solutions. The point of departure is to work with discount bonds:</Text-field>
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<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation>is the price  at time <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIn5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTEY5">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIn5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTEY5</Equation>of a bond that matures on time <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEic0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEic0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=</Equation> . </Text-field>
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<Text-field style="Text" layout="Normal">Obviously we assume that <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbW5HRiQ2JFEiMEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RJiZsZXE7RidGLy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOC8lKXN0cmV0Y2h5R0Y4LyUqc3ltbWV0cmljR0Y4LyUobGFyZ2VvcEdGOC8lLm1vdmFibGVsaW1pdHNHRjgvJSdhY2NlbnRHRjgvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZHLUkjbWlHRiQ2JVEic0YnLyUnaXRhbGljR1EldHJ1ZUYnL0YwUSdpdGFsaWNGJ0YyLUZLNiVRInRGJ0ZORlFGLw==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbW5HRiQ2JFEiMEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RJiZsZXE7RidGLy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOC8lKXN0cmV0Y2h5R0Y4LyUqc3ltbWV0cmljR0Y4LyUobGFyZ2VvcEdGOC8lLm1vdmFibGVsaW1pdHNHRjgvJSdhY2NlbnRHRjgvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZHLUkjbWlHRiQ2JVEic0YnLyUnaXRhbGljR1EldHJ1ZUYnL0YwUSdpdGFsaWNGJ0YyLUZLNiVRInRGJ0ZORlFGLw==</Equation> and that <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation></Text-field>
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<Text-field style="Text" layout="Normal">We can think of <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEic0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIn5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTEY5">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEic0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIn5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTEY5</Equation> as a given date whereas we can introduce a concept <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiVEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiVEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=</Equation> which corresponds to the number of years of maturity of a bond.</Text-field>
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<Text-field style="Text" layout="Normal">The yield to maturity is the internal rate of return of this bond.</Text-field>
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<Text-field style="Text" layout="Normal">We define <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYmLUYsNiVRInRGJ0YvRjItSSNtb0dGJDYtUSIsRicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRkUvJSpzeW1tZXRyaWNHRkUvJShsYXJnZW9wR0ZFLyUubW92YWJsZWxpbWl0c0dGRS8lJ2FjY2VudEdGRS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUYsNiVRIlRGJ0YvRjJGQUZBRkE=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYmLUYsNiVRInRGJ0YvRjItSSNtb0dGJDYtUSIsRicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRkUvJSpzeW1tZXRyaWNHRkUvJShsYXJnZW9wR0ZFLyUubW92YWJsZWxpbWl0c0dGRS8lJ2FjY2VudEdGRS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUYsNiVRIlRGJ0YvRjJGQUZBRkE=</Equation> as the yield to maturity on <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=</Equation> of a bond which matures on <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEic0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEic0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=</Equation> such that the term <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEiVEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSJzRidGL0YyLUY2Ni1RKCZtaW51cztGJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMjIyMjIyMmVtRicvRk5GVi1GLDYlUSJ0RidGL0YyRjk=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEiVEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSJzRidGL0YyLUY2Ni1RKCZtaW51cztGJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMjIyMjIyMmVtRicvRk5GVi1GLDYlUSJ0RidGL0YyRjk=</Equation></Text-field>
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<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYsLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYmLUYsNiVRInRGJ0YvRjItSSNtb0dGJDYtUSIsRicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRkUvJSpzeW1tZXRyaWNHRkUvJShsYXJnZW9wR0ZFLyUubW92YWJsZWxpbWl0c0dGRS8lJ2FjY2VudEdGRS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUYsNiVRIlRGJ0YvRjJGQUZBLUY+Ni1RIj1GJ0ZBRkMvRkdGRUZIRkpGTEZORlAvRlNRLDAuMjc3Nzc3OGVtRicvRlZGam4tSSZtZnJhY0dGJDYoLUkjbW5HRiQ2JFEiMUYnRkEtRiM2JEZYRkEvJS5saW5ldGhpY2tuZXNzR0Ziby8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0Zpby8lKWJldmVsbGVkR0ZFLUYsNiVRJGxvZ0YnL0YwRkVGQS1GPjYtUSJ+RidGQUZDRmhuRkhGSkZMRk5GUEZSL0ZWRlQtRiw2JVEiUEYnRi9GMi1GNjYkLUYjNihGOkY9RlgtRj42LVEiK0YnRkFGQ0ZobkZIRkpGTEZORlAvRlNRLDAuMjIyMjIyMmVtRicvRlZGYXFGOkZBRkEtRiw2I1EhRidGQQ==">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</Equation></Text-field>
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<Text-field style="Text" layout="Normal">These rates are refered to <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiVEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiVEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=</Equation> which is refered as the term structure of interest rates.</Text-field>
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<Text-field style="Text" layout="Normal">The Forward rates will be defined by,</Text-field>
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<Text-field style="Text" layout="Normal"></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYsLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYoLUYsNiVRInRGJ0YvRjItSSNtb0dGJDYtUSIsRicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRkUvJSpzeW1tZXRyaWNHRkUvJShsYXJnZW9wR0ZFLyUubW92YWJsZWxpbWl0c0dGRS8lJ2FjY2VudEdGRS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUYsNiVRIlRGJ0YvRjIvJStleGVjdXRhYmxlR0ZFLyUwZm9udF9zdHlsZV9uYW1lR1EoMkR+TWF0aEYnRkFGQS1GPjYtUSI9RidGQUZDL0ZHRkVGSEZKRkxGTkZQL0ZTUSwwLjI3Nzc3NzhlbUYnL0ZWRl9vLUkobXN1YnN1cEdGJDYnLUY+Ni1RKyZJbnRlZ3JhbDtGJ0ZBL0ZEUSZ1bnNldEYnL0ZHRmhvL0ZJRjEvRktGaG8vRk1GMS9GT0Zoby9GUUZob0ZSL0ZWRlQtRiM2JkY6RmVuRmduRkEtRiM2KEY6LUY+Ni1RIitGJ0ZBRkNGXW9GSEZKRkxGTkZQL0ZTUSwwLjIyMjIyMjJlbUYnL0ZWRmhwRlhGZW5GZ25GQS8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRicvJS9zdWJzY3JpcHRzaGlmdEdGXHEtRiw2JVEiRkYnRi9GMi1GNjYkLUYjNihGOkY9LUYsNiVRJiZ0YXU7RicvRjBGRUZBRmVuRmduRkFGQS1GPjYtUTAmRGlmZmVyZW50aWFsRDtGJ0ZBRmdvRmlvL0ZJRmhvRltwL0ZNRmhvRl1wRl5wRlJGX3AtRiw2JVEnJiM5NjQ7RidGaXFGQUZlbkZB</Equation></Text-field>
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<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
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<Text-field style="Text" layout="Normal">Thus,</Text-field>
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<Text-field style="Text" layout="Normal"></Text-field>
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<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JVEiRkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYmLUYsNiVRInRGJ0YvRjItSSNtb0dGJDYtUSIsRicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRkUvJSpzeW1tZXRyaWNHRkUvJShsYXJnZW9wR0ZFLyUubW92YWJsZWxpbWl0c0dGRS8lJ2FjY2VudEdGRS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUYsNiVRInNGJ0YvRjJGQUZBLUY+Ni1RIj1GJ0ZBRkMvRkdGRUZIRkpGTEZORlAvRlNRLDAuMjc3Nzc3OGVtRicvRlZGam4tSSZtZnJhY0dGJDYoLUY+Ni1RKyZQYXJ0aWFsRDtGJ0ZBL0ZEUSZ1bnNldEYnL0ZHRmNvL0ZJRmNvL0ZLRmNvL0ZNRmNvL0ZPRmNvL0ZRRmNvRlIvRlZGVC1GIzYmLUY+Ni1GYW9GQUZDRmhuRkhGSkZMRk5GUEZSRmpvLUY+Ni1RIn5GJ0ZBRkNGaG5GSEZKRkxGTkZQRlJGam9GWEZBLyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZncC8lKWJldmVsbGVkR0ZFRl9wLUY2NiYtRiM2Jy1GNjYkLUYjNiZGWC1GPjYtUSgmbWludXM7RidGQUZDRmhuRkhGSkZMRk5GUC9GU1EsMC4yMjIyMjIyZW1GJy9GVkZocUY6RkFGQUZfcC1GLDYlUSJSRidGL0YyLUY2NiQtRiM2KEY6Rj1GWEZkcS1GLDYlUSJURidGL0YyRkFGQUZBRkEvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGQQ==">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</Equation></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
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<Text-field style="Text" layout="Normal">The <Font bold="true" italic="true">spot rate</Font> in the instantaneous lending and borrowing rate.</Text-field>
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<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="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">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2LC1GLDYlUSJyRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiQtRiw2JVEidEYnRjRGNy9GOFEnbm9ybWFsRidGQi1JI21vR0YkNi1RIj1GJ0ZCLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZKLyUpc3RyZXRjaHlHRkovJSpzeW1tZXRyaWNHRkovJShsYXJnZW9wR0ZKLyUubW92YWJsZWxpbWl0c0dGSi8lJ2FjY2VudEdGSi8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlktRiw2JVEiUkYnRjRGNy1GOzYkLUYjNiZGPy1GRTYtUSIsRidGQkZIL0ZMRjZGTUZPRlFGU0ZVL0ZYUSYwLjBlbUYnL0ZlblEsMC4zMzMzMzMzZW1GJy1JI21uR0YkNiRRIjBGJ0ZCRkJGQkZELUknbXVuZGVyR0YkNiUtRkU2LVEkbGltRidGQi9GSVEmdW5zZXRGJy9GTEZgcC9GTkZgcC9GUEZgcC9GUkZgcC9GVEY2L0ZWRmBwRmFvL0ZlblEsMC4xNjY2NjY3ZW1GJy1GIzYmLUYsNiVRIlRGJ0Y0RjctRkU2LVEtJnJpZ2h0YXJyb3c7RidGQkZIRksvRk5GNkZPRlFGU0ZVRldGWkZlb0ZCLyUsYWNjZW50dW5kZXJHRkpGZm4tRjs2JC1GIzYmRj9GXW9GW3FGQkZCRkJGK0ZC</Equation></Text-field>
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<Text-field style="Text" layout="Normal">A loan at any time will evolve with certainty given the spot rate. Thus, </Text-field>
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<Text-field style="Text" layout="Normal">The idea will be that this instantaneous rate evolves following a Markovian Process. </Text-field>
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<Text-field style="Text" layout="Normal">This is what is known as one factor assumption.</Text-field>
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<Text-field style="Text" layout="Normal">Namely, we establish that the evolution of the short term rate depends on such rate only.</Text-field>
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<Text-field style="Text" layout="Normal">The process is defined by a stochastic differential equation of the following form</Text-field>
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<Text-field style="Text" layout="Normal">Where <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInRGJ0YvRjIvRjNRJ25vcm1hbEYnRj0tRiw2I1EhRidGPQ==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInRGJ0YvRjIvRjNRJ25vcm1hbEYnRj0tRiw2I1EhRidGPQ==</Equation> is a Wiener Process.</Text-field>
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<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JSFH</Equation></Text-field>
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<Text-field style="Text" italic="true" bold="true" layout="Normal"><Font bold="true" italic="true">Assumption 2.</Font></Text-field>
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<Text-field style="Text" layout="Normal">It is claimed that under rational expectations it can be said that</Text-field>
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<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation></Text-field>
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<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">where \317\226 can have different specifications.</Font></Text-field>
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<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JSFH</Equation></Text-field>
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<Text-field style="Text" layout="Normal"><Font bold="true" italic="true">Assumption 3.</Font></Text-field>
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<Text-field style="Text" layout="Normal">Market efficiency, no transaction costs and rational expectations.</Text-field>
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<Text-field style="Text" layout="Normal"><Font bold="true">Structuring the Problem with Maple</Font></Text-field>
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<Text-field style="Text" layout="Normal">To the extent that <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation> is continuous, we can apply the Ito's lemma in the following way:</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L16663" view="label" executable="true"></Label>); # input placeholder</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">JSFH</Equation></Text-field>
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<Text-field style="Text" layout="Normal">Where the drift and diffusion components are:</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
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<Output>
<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L16665" view="label" executable="true"></Label>); # input placeholder</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUYjNiotSSZtZnJhY0dGJDYoLUYjNigtRi42KC1GIzYmLUkjbW9HRiQ2LVErJlBhcnRpYWxEO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPy8lKXN0cmV0Y2h5R0Y/LyUqc3ltbWV0cmljR0Y/LyUobGFyZ2VvcEdGPy8lLm1vdmFibGVsaW1pdHNHRj8vJSdhY2NlbnRHRj8vJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZOLyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJy8lKXJlYWRvbmx5R0Y/RjotRiM2Ji1GIzYnRjYtSSNtaUdGJDYlUSJ0RicvJSdpdGFsaWNHUSV0cnVlRicvRjtRJ2l0YWxpY0YnRlFGVEY6RlFGVEY6LyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0Ziby8lKWJldmVsbGVkR0Y/LUY3Ni1RMSZJbnZpc2libGVUaW1lcztGJ0Y6Rj1GQEZCRkRGRkZIRkpGTEZPLUYjNigtRmVuNiVRIlBGJ0ZobkZbby1GNzYtUTAmQXBwbHlGdW5jdGlvbjtGJ0Y6Rj1GQEZCRkRGRkZIRkpGTEZPLUkobWZlbmNlZEdGJDYkLUYjNipGWi1GNzYtUSIsRidGOkY9L0ZBRmpuRkJGREZGRkhGSkZML0ZQUSwwLjMzMzMzMzNlbUYnLUZlbjYlUSJzRidGaG5GW29GZ3AtSSVtc3ViR0YkNiUtRmVuNiVRIlVGJ0ZobkZbby1GIzYmLUkjbW5HRiQ2JEZfb0Y6RlFGVEY6LyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGUUZURjpGOkZRRlRGOkZRRlRGOi1JKW1waGFudG9tR0YkNiQtRiM2Ji1GIzYoRmBxLUY3Ni1RIj1GJ0Y6Rj1GQEZCRkRGRkZIRkovRk1RLDAuMjc3Nzc3OGVtRicvRlBGaXItRiM2KC1GZW42JVEjX1hGJ0ZobkZbb0ZfcC1GY3A2JC1GIzYmRlpGUUZURjpGOkZRRlRGOkZRRlRGOkZRRlRGOi8lLGNvbnN0cmFpbnRzR1EsaGVpZ2h0LW9ubHlGJy9GXm9GXXJGYG9GY29GZW8tSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdRJjAuM2VtRicvJSZkZXB0aEdGXXQvJSpsaW5lYnJlYWtHUSVhdXRvRictRjc2LVEpJnZlcmJhcjtGJ0Y6Rj1GQC9GQ0ZqbkZERkZGSEZKL0ZNUSwwLjExMTExMTFlbUYnL0ZQRlt1LUZpczYmRlt0L0ZfdFEmMC4xZW1GJ0ZhdEZjdC1GLjYoLUZfcjYkRjBGZHNGYXJGZ3NGYG9GY29GZW9GUUZURjotRjc2LVEiK0YnRjpGPUZARkJGREZGRkhGSi9GTVEsMC4yMjIyMjIyZW1GJy9GUEZpdS1GIzYmLUYjNigtRmVuNiVRImZGJ0ZobkZbb0ZfcC1GY3A2JC1GIzYoRltzRmdwRlpGUUZURjpGOkZRRlRGOkZnby1GY3A2JC1GIzYqLUYuNigtRiM2KC1GLjYoRjQtRiM2Ji1GIzYnRjZGYHFGUUZURjpGUUZURjpGXW9GYG9GY29GZW9GZ29Gam9GUUZURjpGXnJGZ3NGYG9GY29GZW9GaHNGZnRGXXUtRi42KC1GX3I2JEZcd0Zkc0ZhckZnc0Zgb0Zjb0Zlb0ZRRlRGOkY6RjpGZXUtRiM2KC1GLjYoRmhxLUZpcTYkUSIyRidGOkZdb0Zgb0Zjb0Zlb0Znby1GIzYmLUklbXN1cEdGJDYlLUYjNigtRmVuNiVRJyYjOTYxO0YnL0ZpbkY/RjpGX3BGYnZGUUZURjpGXHgvJTFzdXBlcnNjcmlwdHNoaWZ0R0ZdckZnby1GY3A2JC1GIzYqLUYuNigtRiM2KC1GLjYoLUYjNiYtRmJ4NiVGNkZceEZqeEZRRlRGOi1GIzYmLUYjNidGNi1GYng2JUZgcUZceEZqeEZRRlRGOkZRRlRGOkZdb0Zgb0Zjb0Zlb0Znb0Zqb0ZRRlRGOkZeckZnc0Zgb0Zjb0Zlb0Zoc0ZmdEZddS1GLjYoLUZfcjYkRmJ5RmRzRmFyRmdzRmBvRmNvRmVvRlFGVEY6RjpGOkZRRlRGOkY6">LCgtSSVldmFsRyUqcHJvdGVjdGVkRzYkLUklZGlmZkdGJTYkLUkiUEc2IjYlSSJ0R0YsSSJzR0YsJkkiVUc2Iy9JJ19sb2NhbEdGJUksX24xODg5Njc2NDhHRiw2IyIiIkYuPCMvRjAtSSNfWEc2JEYlSTNfU3RvY2hhc3RpY1Byb2Nlc3NHRiw2I0YuRjcqJi1JImZHRiw2JEY6Ri5GNy1GJDYkLUYoNiRGKkYwRjhGN0Y3KigjRjciIiNGNyktSSRyaG9HRixGQkZJRjctRiQ2JC1GKDYkRkVGMEY4RjdGNw==</Equation></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
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<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L16671" view="label" executable="true"></Label>); # input placeholder</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KiYtSSRyaG9HNiI2JC1JI19YRzYkJSpwcm90ZWN0ZWRHSTNfU3RvY2hhc3RpY1Byb2Nlc3NHRiU2I0kidEdGJUYtIiIiLUklZXZhbEdGKjYkLUklZGlmZkdGKjYkLUkiUEdGJTYlRi1JInNHRiUmSSJVRzYjL0knX2xvY2FsR0YqSSxfbjM2Mjk0MTYzMkdGJTYjRi5GOTwjL0Y5RidGLg==</Equation></Text-field>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">JSFH</Equation></Text-field>
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<Input>
<Text-field style="Text" layout="Normal">We can rewrite these results in a more friendly and compact format:</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYwLUkjbWlHRiQ2JVEjZFBGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSI9RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtRjY2LVEifkYnRjlGO0Y+RkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTkZTLUYsNiVRIlBGJ0YvRjItRjY2LVEnJnNkb3Q7RidGOUY7Rj5GQEZCRkRGRkZIRlJGVC1GLDYlUScmIzk1NjtGJy9GMEY9RjktSShtZmVuY2VkR0YkNiQtRiM2Ji1GLDYlUSJ0RidGL0YyLUY2Ni1RIixGJ0Y5RjsvRj9GMUZARkJGREZGRkhGUi9GTlEsMC4zMzMzMzMzZW1GJy1GLDYlUSJzRidGL0YyRjlGOS1GNjYtUSgmbWludXM7RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSwwLjIyMjIyMjJlbUYnL0ZORl5wRlVGWC1GLDYlUScmIzk2MztGJ0ZobkY5RmluLUYsNiVRI2R6RidGL0YyRjk=">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</Equation></Text-field>
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<Input>
<Text-field style="Text" layout="Normal"></Text-field>
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<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16676" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">where,</Text-field>
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<Input>
<Text-field style="Text" layout="Normal"></Text-field>
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<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16680" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation></Text-field>
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<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JSFH</Equation></Text-field>
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<Text-field style="Text" layout="Normal">We move ahead now to talk about a non-arbitrage condition.</Text-field>
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<Text-field style="Text" layout="Normal"></Text-field>
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<Text-field style="Text" layout="Normal">We assume that a person issues a bond with maturity on  <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEjczFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSJ+RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkxGOQ==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEjczFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSJ+RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkxGOQ==</Equation>and buys a bond with maturity in <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEjczJGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSIuRicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkwtRjY2LVEifkYnRjlGO0Y+RkBGQkZERkZGSEZKRk1GOQ==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEjczJGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSIuRicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkwtRjY2LVEifkYnRjlGO0Y+RkBGQkZERkZGSEZKRk1GOQ==</Equation> The total worth is <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation>  </Text-field>
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<Text-field style="Text" layout="Normal">The value of the portfolio has to evolve following,</Text-field>
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<Text-field style="Text" layout="Normal">If the amounts are chosen in a way that they are proportional to their respective volatilities, then the volatility term disappears and we end up with the following expression.</Text-field>
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<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYsLUkjbWlHRiQ2JVEjZFdGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSI9RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtRiw2JVEiV0YnRi9GMi1GNjYtUScmc2RvdDtGJ0Y5RjtGPkZARkJGREZGRkgvRktRJjAuMGVtRicvRk5GVi1GNjYtUSIoRidGOS9GPEYxRj4vRkFGMUZCRkRGRkZIL0ZLUSwwLjE2NjY2NjdlbUYnL0ZORmhuLUkmbWZyYWNHRiQ2KC1GIzYkLUkobWZlbmNlZEdGJDYkLUYjNi9GWC1GLDYlUSUmbXU7RicvRjBGPUY5LUZgbzYkLUYjNictRiw2JVEidEYnRi9GMi1GNjYtUSIsRidGOUY7L0Y/RjFGQEZCRkRGRkZIRlUvRk5RLDAuMzMzMzMzM2VtRictRiw2JVEic0YnRi9GMi1GYG82Ji1GIzYkLUkjbW5HRiQ2JFEiMkYnRjlGOUY5LyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnRjlGOUZSLUYsNiVRKCZzaWdtYTtGJ0Znb0Y5LUZgbzYkLUYjNidGXHBGX3BGZXAtRmBvNiYtRiM2JC1GXXE2JFEiMUYnRjlGOUY5RmBxRmNxRjlGOS1GNjYtUSgmbWludXM7RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSwwLjIyMjIyMjJlbUYnL0ZORmhyRmRvRmlxRlJGZnFGaG9GOUY5RjktRiM2NkZmcUZYRlxwRl9wRmVwLUY2Ni1GYnFGOUZlbkY+RmZuRkJGREZGRkhGZ25GaW5GYXItRjY2LUZlcUY5RmVuRj5GZm5GQkZERkZGSEZnbi9GTlEsMC4xMTExMTExZW1GJy1GNjYtUSIpRidGOUZlbkY+RmZuRkJGREZGRkhGZ25GaW4tRjY2LVEqJnVtaW51czA7RidGOUY7Rj5GQEZCRkRGRkZIRmdyRmlyRmZxRlhGXHBGX3BGZXBGXHNGXHFGXnNGYnNGOS8lLmxpbmV0aGlja25lc3NHRmNyLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRlx0LyUpYmV2ZWxsZWRHRj1GYnMtRiw2JVEjZHRGJ0YvRjItRjY2LVEiO0YnRjlGO0ZicEZARkJGREZGRkhGVUZNRjk=">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</Equation></Text-field>
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<Text-field style="Text" layout="Normal">We already new that </Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
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<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JSFH</Equation></Text-field>
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<Text-field style="Text" layout="Normal">We define a variable that corresponds to that ration for all values of <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEic0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEic0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=</Equation></Text-field>
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<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation></Text-field>
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<Text-field style="Text" layout="Normal">We can rearrange terms to get a structure like this,</Text-field>
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<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation></Text-field>
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<Text-field style="Text" layout="Normal">We already had a definition for <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NTY7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NTY7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy</Equation> and <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NjM7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NjM7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy</Equation>.</Text-field>
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<Text-field style="Text" layout="Normal">We use them to get to a partial differential equation:</Text-field>
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<Text-field style="Text" layout="Normal"></Text-field>
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<Text-field style="Text" layout="Normal"></Text-field>
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<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation></Text-field>
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<Text-field style="Text" layout="Normal">This PDE is the term structure.</Text-field>
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<Text-field style="Text" layout="Normal">The boundary condition is 
<Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation></Text-field>
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<Section collapsed="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 2" layout="Heading 2">2.3 Partial Differential Equations: a Refresher</Text-field></Title><Presentation-Block>
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<Text-field style="Heading 3" layout="Heading 3">2.3.1 Main types and solutions of Partial Differetnial Equations</Text-field></Title><Presentation-Block>
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<Text-field style="Heading 4" layout="Heading 4">2.3.1.1 Parabolic Partial Differential Equations</Text-field></Title><Presentation-Block>
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<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JSFH</Equation></Text-field>
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</Group></Presentation-Block><Table interior="group" showinput="true" alignment="left" exterior="all" width="81.27159640635799%" labelreference="L16725" showlabel="true" captionalignment="0" title="" order="row" drawcaption="false" randomized="false" captionposition="1" plotalignlists="" pagebreak="cell" postexecute="insert" showgroup="true"><Table-Column weight="441" separator="true"></Table-Column><Table-Column weight="735" separator="true"></Table-Column><Table-Row align="top" separator="true"><Table-Cell columnspan="2" backgroundstyle="1" rowspan="1" padding="5" fillcolor="[102,102,153]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L21691" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" foreground="[255,255,255]" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStmb3JlZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">JSFH</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L21693" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" foreground="[255,255,255]" layout="Normal" alignment="centred"><Font foreground="[255,255,255]">PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L21694" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" foreground="[255,255,255]" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStmb3JlZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">JSFH</Equation></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell columnspan="2" backgroundstyle="1" rowspan="1" padding="5" fillcolor="[204,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16726" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JSFH</Equation></Text-field>
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</Group></Presentation-Block><Presentation-Block><CodeEditor-ExecGroup view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L7" applyint="true" applyrational="true" display="code"><EC-CodeEditor id="CodeEditRegion0" visible="false" pixel-width="500" pixel-height="200" code-language="text/maple" autoexpand="true" wrapping="false" show-border="true" code-line-numbers="true">#RESTART AND LOAD PACKAGES
restart:
with(PDETools):</EC-CodeEditor></CodeEditor-ExecGroup></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16728" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal">The form of a parabolic PDE is:</Text-field>
</Input>
</Group></Presentation-Block></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16729" drawlabel="true" applyint="true" applyrational="true" applyexponent="false" redirect-target="L16733">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
</Input>
<Output>
<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
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<Group view="presentation" hide-input="true" hide-output="false" inline-output="false" labelreference="L16733" drawlabel="true" applyint="true" applyrational="true" applyexponent="false" redirect-source="L16729">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L16729" view="label" executable="true"></Label>); # input placeholder</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUYjNiYtRiM2KC1JJm1mcmFjR0YkNigtRiM2Ji1JI21vR0YkNi1RKyZQYXJ0aWFsRDtGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC8lK2ZvcmVncm91bmRHUShbMCwwLDBdRicvJSlyZWFkb25seUdGPUY4LUYjNiYtRiM2J0Y0LUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnL0Y5USdpdGFsaWNGJ0ZPRlJGOEZPRlJGOC8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGYG8vJSliZXZlbGxlZEdGPS1GNTYtUTEmSW52aXNpYmxlVGltZXM7RidGOEY7Rj5GQEZCRkRGRkZIRkpGTS1GIzYoLUZZNiVRIlBGJ0ZmbkZpbi1GNTYtUTAmQXBwbHlGdW5jdGlvbjtGJ0Y4RjtGPkZARkJGREZGRkhGSkZNLUkobWZlbmNlZEdGJDYkLUYjNihGWC1GNTYtUSIsRidGOEY7L0Y/RmhuRkBGQkZERkZGSEZKL0ZOUSwwLjMzMzMzMzNlbUYnLUZZNiVRInJGJ0ZmbkZpbkZPRlJGOEY4Rk9GUkY4Rk9GUkY4LUY1Ni1RIitGJ0Y4RjtGPkZARkJGREZGRkgvRktRLDAuMjIyMjIyMmVtRicvRk5GYnEtRiM2Ji1GWTYlUScmIzk1MjtGJy9GZ25GPUY4RmVvLUZhcDYkLUYjNigtRjA2KC1GIzYmLUklbXN1cEdGJDYlRjQtSSNtbkdGJDYkUSIyRidGOC8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGT0ZSRjgtRiM2Ji1GIzYnRjQtRmNyNiVGW3FGZXJGaXJGT0ZSRjhGT0ZSRjhGW29GXm9GYW9GY29GZW9GaG9GT0ZSRjhGOEY4RjgtRjU2LVEiPUYnRjhGO0Y+RkBGQkZERkZGSC9GS1EsMC4yNzc3Nzc4ZW1GJy9GTkZmcy1GZnI2JEZbc0Y4Rk9GUkY4">LywmLUklZGlmZkclKnByb3RlY3RlZEc2JC1JIlBHNiI2JEkidEdGKkkickdGKkYsIiIiKiZJJnRoZXRhR0YqRi4tRiU2JC1GJTYkRihGLUYtRi5GLiIiIQ==</Equation></Text-field>
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</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16734" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">JSFH</Equation></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16730" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal">The process of solving in Maple goes as follows:</Text-field>
</Input>
</Group></Presentation-Block></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16731" drawlabel="true" applyint="true" applyrational="true" applyexponent="false" redirect-target="L16735">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JVEucGFyYWJvbGljX3NvbEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUYsNiVRKHBkc29sdmVGJ0YvRjItSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSpwYXJhYm9saWNGJ0YvRjJGOUY5LUY2Ni1RIjtGJ0Y5RjsvRj9GMUZARkJGREZGRkgvRktRJjAuMGVtRidGTS8lK2V4ZWN1dGFibGVHRj1GOQ==">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</Equation></Text-field>
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<Output>
<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
</Output>
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<Group view="presentation" hide-input="true" hide-output="false" inline-output="false" labelreference="L16735" drawlabel="true" applyint="true" applyrational="true" applyexponent="false" redirect-source="L16731">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L16731" view="label" executable="true"></Label>); # input placeholder</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LUksUERFU29sU3RydWNHJSpwcm90ZWN0ZWRHNiQvLUkiUEc2IjYkSSJ0R0YpSSJyR0YpKiYtSSRfRjFHRik2I0YrIiIiLUkkX0YyR0YpNiNGLEYxNyM8JC8tSSVkaWZmR0YkNiRGLkYrKiYmSSNfY0c2JEYkSShfc3lzbGliR0YpNiNGMUYxRi5GMS8tRjk2JC1GOTYkRjJGLEYsLCQqKEY8RjFGMkYxSSZ0aGV0YUdGKSEiIkZJ</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16736" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">JSFH</Equation></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16741" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">We notice here that the problem is solved by a separation of two ordinary differential equations that multiply each other.</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16740" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Maple will be able to build a solution based on this fact.</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16738" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16739" drawlabel="true" applyint="true" applyrational="true" applyexponent="false" redirect-target="L16742">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
</Input>
<Output>
<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
</Output>
</Group>
<Group view="presentation" hide-input="true" hide-output="false" inline-output="false" labelreference="L16742" drawlabel="true" applyint="true" applyrational="true" applyexponent="false" redirect-source="L16739">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L16739" view="label" executable="true"></Label>); # input placeholder</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly1JIlBHNiI2JEkidEdGJUkickdGJSooSSRfQzFHRiUiIiItSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2IyomSSJrR0YlRitGJ0YrRissJiomSSRfQzJHRiVGKy1JJHNpbkdGLjYjKigpSSZ0aGV0YUdGJSNGKyIiIyEiIilGM0Y9RitGKEYrRitGKyomSSRfQzNHRiVGKy1JJGNvc0dGLkY5RitGK0Yr</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16743" drawlabel="true" applyint="true" applyrational="true" applyexponent="false" redirect-target="L16744">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYtLUkjbWlHRiQ2JVE2cGFyYWJvbGljX2dlbmVyYWxfc29sRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEqJmNvbG9uZXE7RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtRiw2JVEiUEYnRi9GMi1JKG1mZW5jZWRHRiQ2JC1GIzYmLUYsNiVRInRGJ0YvRjItRjY2LVEiLEYnRjlGOy9GP0YxRkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTlEsMC4zMzMzMzMzZW1GJy1GLDYlUSJyRidGL0YyRjlGOS1GNjYtUSI9RidGOUY7Rj5GQEZCRkRGRkZIRkpGTS1GNjYtUSJ+RidGOUY7Rj5GQEZCRkRGRkZIRmhuL0ZORmluLUYsNiVRJXN1YnNGJ0YvRjItRlM2JC1GIzYoLUYsNiVRLnBhcmFib2xpY19zb2xGJ0YvRjJGWkZiby1GLDYlUSRpbnRGJ0YvRjItRlM2JC1GIzYvLUYsNiVRIkFGJ0YvRjItRlM2JC1GIzYkLUYsNiVRImtGJ0YvRjJGOUY5LUY2Ni1RJyZzZG90O0YnRjlGO0Y+RkBGQkZERkZGSEZobkZlb0ZPRlJGWkZib0ZecUZfby1GLDYlUSJhRidGL0YyLUY2Ni1RIy4uRidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSwwLjIyMjIyMjJlbUYnRmVvLUYsNiVRImJGJ0YvRjJGOUY5RjlGOS1GNjYtUSI7RidGOUY7RmduRkBGQkZERkZGSEZobkZNLyUrZXhlY3V0YWJsZUdGPUY5">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</Equation></Text-field>
</Input>
<Output>
<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
</Output>
</Group>
<Group view="presentation" hide-input="true" hide-output="false" inline-output="false" labelreference="L16744" drawlabel="true" applyint="true" applyrational="true" applyexponent="false" redirect-source="L16743">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L16743" view="label" executable="true"></Label>); # input placeholder</Text-field>
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<Output>
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<Text-field style="Text" layout="Normal">We notice here that <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRImtGJ0YvRjIvRjNRJ25vcm1hbEYnRj0tRiw2I1EhRidGPQ==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRImtGJ0YvRjIvRjNRJ25vcm1hbEYnRj0tRiw2I1EhRidGPQ==</Equation> can be an arbitrary function.</Text-field>
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<Text-field style="Text" layout="Normal">We finally test wether this solution actually solves the PDE.</Text-field>
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<Text-field style="Heading 4" layout="Heading 4">2.3.1.2 Hyperbolic Partial Differential Equations</Text-field></Title><Presentation-Block>
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<Text-field style="Text" foreground="[255,255,255]" layout="Normal" alignment="centred"><Font foreground="[255,255,255]">PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS</Font></Text-field>
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restart:
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<Text-field style="Text" layout="Normal">The form of a Hyperbolic PDE is:</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY0LUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLUkjbWlHRiQ2JVEraHlwZXJib2xpY0YnLyUnaXRhbGljR1EldHJ1ZUYnL0YwUSdpdGFsaWNGJy1GLDYtUSomY29sb25lcTtGJ0YvRjJGNUY3RjlGO0Y9Rj8vRkJRLDAuMjc3Nzc3OGVtRicvRkVGUy1JJm1mcmFjR0YkNigtRiM2JC1JJW1zdXBHRiQ2JS1GLDYtUSsmUGFydGlhbEQ7RidGL0YyRjVGN0Y5RjtGPUY/RkFGRC1GIzYkLUkjbW5HRiQ2JFEiMkYnRi9GLy8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGLy1GIzYmRmduRistRmVuNiUtRkc2JVEidEYnRkpGTUZqbkZgb0YvLyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZfcC8lKWJldmVsbGVkR0Y0RistRkc2JVEiUEYnRkpGTS1JKG1mZW5jZWRHRiQ2JC1GIzYmRmdvLUYsNi1RIixGJ0YvRjIvRjZGTEY3RjlGO0Y9Rj9GQS9GRVEsMC4zMzMzMzMzZW1GJy1GRzYlUSJyRidGSkZNRi9GLy1GLDYtUSgmbWludXM7RidGL0YyRjVGN0Y5RjtGPUY/L0ZCUSwwLjIyMjIyMjJlbUYnL0ZFRmlxLUZlbjYlLUZHNiVRKCZ0aGV0YTtGJy9GS0Y0Ri9Gam5GYG8tRiw2LVEnJnNkb3Q7RidGL0YyRjVGN0Y5RjtGPUY/RkFGRC1GVjYoRlgtRiM2JkZnbkYrLUZlbjYlRmJxRmpuRmBvRi9Gam9GXXBGYHBGYnBGZHBGZ3AtRiw2LVEiPUYnRi9GMkY1RjdGOUY7Rj1GP0ZSRlQtRl1vNiRGYm9GLy1GLDYtUSI7RidGL0YyRl9xRjdGOUY7Rj1GP0ZBRlQvJStleGVjdXRhYmxlR0Y0Ri8=</Equation></Text-field>
</Input>
<Output>
<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
</Output>
</Group>
<Group view="presentation" hide-input="true" hide-output="false" inline-output="false" labelreference="L16762" drawlabel="true" applyint="true" applyrational="true" applyexponent="false" redirect-source="L16758">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L16758" view="label" executable="true"></Label>); # input placeholder</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LywmLUklZGlmZkclKnByb3RlY3RlZEc2JC1GJTYkLUkiUEc2IjYkSSJ0R0YsSSJyR0YsRi5GLiIiIiomKUkmdGhldGFHRiwiIiNGMC1GJTYkLUYlNiRGKkYvRi9GMCEiIiIiIQ==</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16763" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">JSFH</Equation></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16759" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal">The process of solving in Maple goes as follows:</Text-field>
</Input>
</Group></Presentation-Block></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16760" drawlabel="true" applyint="true" applyrational="true" applyexponent="false" redirect-target="L16764">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
</Input>
<Output>
<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
</Output>
</Group>
<Group view="presentation" hide-input="true" hide-output="false" inline-output="false" labelreference="L16764" drawlabel="true" applyint="true" applyrational="true" applyexponent="false" redirect-source="L16760">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L16760" view="label" executable="true"></Label>); # input placeholder</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly1JIlBHNiI2JEkidEdGJUkickdGJSwmLUkkX0YxR0YlNiMsJiomRiciIiJJJnRoZXRhR0YlRi8hIiJGKEYxRi8tSSRfRjJHRiU2IywmRi5GMUYoRi9GLw==</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16765" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">JSFH</Equation></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16769" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Here we notice that the solution will be the sum of two arbitrary functions.</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16768" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">We produce a particular solution and a general solution as follows:</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16766" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16767" drawlabel="true" applyint="true" applyrational="true" applyexponent="false" redirect-target="L16770">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
</Input>
<Output>
<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
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</Group>
<Group view="presentation" hide-input="true" hide-output="false" inline-output="false" labelreference="L16770" drawlabel="true" applyint="true" applyrational="true" applyexponent="false" redirect-source="L16767">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L16767" view="label" executable="true"></Label>); # input placeholder</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUYjNigtSSNtaUdGJDYlUSJQRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvRjVRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y/LyUpc3RyZXRjaHlHRj8vJSpzeW1tZXRyaWNHRj8vJShsYXJnZW9wR0Y/LyUubW92YWJsZWxpbWl0c0dGPy8lJ2FjY2VudEdGPy8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRk4tSShtZmVuY2VkR0YkNiQtRiM2KC1GLjYlUSJ0RidGMUY0LUY4Ni1RIixGJ0Y7Rj0vRkFGM0ZCRkRGRkZIRkpGTC9GUFEsMC4zMzMzMzMzZW1GJy1GLjYlUSJyRidGMUY0LyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJy8lKXJlYWRvbmx5R0Y/RjtGO0Zcb0Zfb0Y7LUY4Ni1RIj1GJ0Y7Rj1GQEZCRkRGRkZIRkovRk1RLDAuMjc3Nzc3OGVtRicvRlBGZW8tRiM2Ji1GIzYoLUYuNiVRJyYjOTQ1O0YnL0YyRj9GO0Y3LUZSNiQtRiM2Ji1GIzYnLUY4Ni1RKiZ1bWludXMwO0YnRjtGPUZARkJGREZGRkhGSi9GTVEsMC4yMjIyMjIyZW1GJy9GUEZpcC1GIzYmRlYtRjg2LVExJkludmlzaWJsZVRpbWVzO0YnRjtGPUZARkJGREZGRkhGSkZMRk8tRi42JVEnJiM5NTI7RidGXnBGO0Y7LUY4Ni1RKCZtaW51cztGJ0Y7Rj1GQEZCRkRGRkZIRkpGaHBGanBGaW5GO0Zcb0Zfb0Y7RjtGXG9GX29GOy1GODYtUSIrRidGO0Y9RkBGQkZERkZGSEZKRmhwRmpwLUYjNigtRi42JVEnJiM5NDY7RidGXnBGO0Y3LUZSNiQtRiM2Ji1GIzYnRmVwRltxRmZxRmluRjtGXG9GX29GO0Y7RlxvRl9vRjtGO0Zcb0Zfb0Y7">Ly1JIlBHNiI2JEkidEdGJUkickdGJSwmLUkmYWxwaGFHRiU2IywmKiZGJyIiIkkmdGhldGFHRiVGLyEiIkYoRjFGLy1JJWJldGFHRiU2IywmRi5GMUYoRi9GLw==</Equation></Text-field>
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</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16771" drawlabel="true" applyint="true" applyrational="true" applyexponent="false" redirect-target="L16772">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
</Input>
<Output>
<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
</Output>
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<Group view="presentation" hide-input="true" hide-output="false" inline-output="false" labelreference="L16772" drawlabel="true" applyint="true" applyrational="true" applyexponent="false" redirect-source="L16771">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L16771" view="label" executable="true"></Label>); # input placeholder</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly1JIlBHNiI2JEkidEdGJUkickdGJS1JJGludEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYkKiYtSSJBR0YlNiNJImtHRiUiIiIsJi1JJmFscGhhR0YlNiMsJiomRidGNEkmdGhldGFHRiVGNCEiIkYoRjxGNC1JJWJldGFHRiU2IywmRjpGPEYoRjRGNEY0L0YzO0kiYUdGJUkiYkdGJQ==</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16773" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">JSFH</Equation></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16774" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal">Once again, we verify that the proposed solution actually solves the partial differential equation.</Text-field>
</Input>
</Group></Presentation-Block></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16775" drawlabel="true" applyint="true" applyrational="true" applyexponent="false" redirect-target="L16776">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEoY29tYmluZUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRJmRzdWJzRidGL0YyLUY2NiQtRiM2Jy1GLDYlUS9oeXBlcmJvbGljX3NvbEYnRi9GMi1JI21vR0YkNi1RIixGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGTC8lKnN5bW1ldHJpY0dGTC8lKGxhcmdlb3BHRkwvJS5tb3ZhYmxlbGltaXRzR0ZMLyUnYWNjZW50R0ZMLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRkU2LVEifkYnRkhGSi9GTkZMRk9GUUZTRlVGV0ZZL0ZnbkZlbi1GLDYlUStoeXBlcmJvbGljRidGL0YyRkhGSEZIRkgtRkU2LVEiO0YnRkhGSkZNRk9GUUZTRlVGV0ZZL0ZnblEsMC4yNzc3Nzc4ZW1GJy8lK2V4ZWN1dGFibGVHRkxGSA==">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</Equation></Text-field>
</Input>
<Output>
<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
</Output>
</Group>
<Group view="presentation" hide-input="true" hide-output="false" inline-output="false" labelreference="L16776" drawlabel="true" applyint="true" applyrational="true" applyexponent="false" redirect-source="L16775">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L16775" view="label" executable="true"></Label>); # input placeholder</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">LyIiIUYj</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16777" drawlabel="true" applyint="true" applyrational="true" applyexponent="false" redirect-target="L16778">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
</Input>
<Output>
<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
</Output>
</Group>
<Group view="presentation" hide-input="true" hide-output="false" inline-output="false" labelreference="L16778" drawlabel="true" applyint="true" applyrational="true" applyexponent="false" redirect-source="L16777">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L16777" view="label" executable="true"></Label>); # input placeholder</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">IiIh</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16779" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">JSFH</Equation></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row></Table><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L8681" drawlabel="true" redirect-target="L8682">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">JSFH</Equation></Text-field>
</Input>
</Group></Presentation-Block>
</Section>
<Section collapsed="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 4" layout="Heading 4">2.3.1.3 Elliptic Partial Differential Equation</Text-field></Title><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L8705" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JSFH</Equation></Text-field>
</Input>
</Group></Presentation-Block><Table interior="group" showinput="true" alignment="left" exterior="all" width="81.61713890808569%" labelreference="L16780" showlabel="true" captionalignment="0" title="" order="row" drawcaption="false" randomized="false" captionposition="1" plotalignlists="" pagebreak="cell" postexecute="insert" showgroup="true"><Table-Column weight="449" separator="true"></Table-Column><Table-Column weight="732" separator="true"></Table-Column><Table-Row align="top" separator="true"><Table-Cell columnspan="2" backgroundstyle="1" rowspan="1" padding="5" fillcolor="[102,102,153]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L21713" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" foreground="[255,255,255]" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStmb3JlZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L21711" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" foreground="[255,255,255]" layout="Normal" alignment="centred"><Font foreground="[255,255,255]">ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L21710" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" foreground="[255,255,255]" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStmb3JlZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell columnspan="2" backgroundstyle="1" rowspan="1" padding="5" fillcolor="[204,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L21712" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block><CodeEditor-ExecGroup view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L21709" applyint="true" applyrational="true" display="code"><EC-CodeEditor id="CodeEditRegion2" visible="false" pixel-width="500" pixel-height="200" code-language="text/maple" autoexpand="true" wrapping="false" show-border="true" code-line-numbers="true">#RESTART AND LOAD PACKAGES
restart:
with(PDETools):</EC-CodeEditor></CodeEditor-ExecGroup></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16783" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16784" drawlabel="true" applyint="true" applyrational="true" applyexponent="false" redirect-target="L16788">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYxLUkjbWlHRiQ2JVEpZWxsaXB0aWNGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSomY29sb25lcTtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JJm1mcmFjR0YkNigtRiM2JC1JJW1zdXBHRiQ2JS1GNjYtUSsmUGFydGlhbEQ7RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSYwLjBlbUYnL0ZORmVuLUYjNiQtSSNtbkdGJDYkUSIyRidGOUY5LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0Y5LUYjNiZGVy1GNjYtUSJ+RidGOUY7Rj5GQEZCRkRGRkZIRlpGZm4tRlU2JS1GLDYlUSJ0RidGL0YyRmduRl1vRjkvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRl9wLyUpYmV2ZWxsZWRHRj1GYm8tRiw2JVEiUEYnRi9GMi1JKG1mZW5jZWRHRiQ2JC1GIzYmRmdvLUY2Ni1RIixGJ0Y5RjsvRj9GMUZARkJGREZGRkhGWi9GTlEsMC4zMzMzMzMzZW1GJy1GLDYlUSJyRidGL0YyRjlGOS1GNjYtUSIrRidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSwwLjIyMjIyMjJlbUYnL0ZORmlxLUZQNihGUi1GIzYmRldGYm8tRlU2JUZicUZnbkZdb0Y5RmpvRl1wRmBwRmJwRmRwRmdwLUY2Ni1RIj1GJ0Y5RjtGPkZARkJGREZGRkhGSkZNLUZqbjYkRl9vRjktRjY2LVEiO0YnRjlGO0ZfcUZARkJGREZGRkhGWkZNLyUrZXhlY3V0YWJsZUdGPUY5">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</Equation></Text-field>
</Input>
<Output>
<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
</Output>
</Group>
<Group view="presentation" hide-input="true" hide-output="false" inline-output="false" labelreference="L16788" drawlabel="true" applyint="true" applyrational="true" applyexponent="false" redirect-source="L16784">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L16784" view="label" executable="true"></Label>); # input placeholder</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LywmLUklZGlmZkclKnByb3RlY3RlZEc2JC1GJTYkLUkiUEc2IjYkSSJ0R0YsSSJyR0YsRi5GLiIiIi1GJTYkLUYlNiRGKkYvRi9GMCIiIQ==</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16789" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16785" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16786" drawlabel="true" applyint="true" applyrational="true" applyexponent="false" redirect-target="L16790">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
</Input>
<Output>
<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
</Output>
</Group>
<Group view="presentation" hide-input="true" hide-output="false" inline-output="false" labelreference="L16790" drawlabel="true" applyint="true" applyrational="true" applyexponent="false" redirect-source="L16786">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L16786" view="label" executable="true"></Label>); # input placeholder</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly1JIlBHNiI2JEkidEdGJUkickdGJSwmLUkkX0YxR0YlNiMsJkYoIiIiKiYsJF4jRi5GLkYuRidGLiEiIkYuLUkkX0YyR0YlNiMsJkYoRi4qJkYxRi5GJ0YuRi5GLg==</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16791" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16795" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Here we notice that the solution will be the sum of two arbitrary functions.</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16794" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Here the solutions are functions of a complex variable and its conjugate.</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16796" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">We produce a particular solution and a general solution as follows:</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16792" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16793" drawlabel="true" applyint="true" applyrational="true" applyexponent="false" redirect-target="L16797">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
</Input>
<Output>
<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
</Output>
</Group>
<Group view="presentation" hide-input="true" hide-output="false" inline-output="false" labelreference="L16797" drawlabel="true" applyint="true" applyrational="true" applyexponent="false" redirect-source="L16793">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L16793" view="label" executable="true"></Label>); # input placeholder</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly1JIlBHNiI2JEkidEdGJUkickdGJSwmLUkmYWxwaGFHRiU2IywmRigiIiIqJiwkXiNGLkYuRi5GJ0YuISIiRi4tSSViZXRhR0YlNiMsJkYoRi4qJkYxRi5GJ0YuRi5GLg==</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16798" drawlabel="true" applyint="true" applyrational="true" applyexponent="false" redirect-target="L16799">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
</Input>
<Output>
<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
</Output>
</Group>
<Group view="presentation" hide-input="true" hide-output="false" inline-output="false" labelreference="L16799" drawlabel="true" applyint="true" applyrational="true" applyexponent="false" redirect-source="L16798">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L16798" view="label" executable="true"></Label>); # input placeholder</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly1JIlBHNiI2JEkidEdGJUkickdGJS1JJGludEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYkKiYtSSJBR0YlNiNJImtHRiUiIiIsJi1JJmFscGhhR0YlNiMsJkYoRjQqJiwkXiNGNEY0RjRGJ0Y0ISIiRjQtSSViZXRhR0YlNiMsJkYoRjQqJkY8RjRGJ0Y0RjRGNEY0L0YzO0kiYUdGJUkiYkdGJQ==</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16800" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16801" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal">Once again, we verify that the proposed solution actually solves the partial differential equation.</Text-field>
</Input>
</Group></Presentation-Block></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16802" drawlabel="true" applyint="true" applyrational="true" applyexponent="false" redirect-target="L16803">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
</Input>
<Output>
<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
</Output>
</Group>
<Group view="presentation" hide-input="true" hide-output="false" inline-output="false" labelreference="L16803" drawlabel="true" applyint="true" applyrational="true" applyexponent="false" redirect-source="L16802">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L16802" view="label" executable="true"></Label>); # input placeholder</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">LyIiIUYj</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16804" drawlabel="true" applyint="true" applyrational="true" applyexponent="false" redirect-target="L16805">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
</Input>
<Output>
<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
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<Group view="presentation" hide-input="true" hide-output="false" inline-output="false" labelreference="L16805" drawlabel="true" applyint="true" applyrational="true" applyexponent="false" redirect-source="L16804">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L16804" view="label" executable="true"></Label>); # input placeholder</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">IiIh</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16806" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
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</Group></Presentation-Block></Table-Cell></Table-Row></Table><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L8721" drawlabel="true" redirect-target="L8723">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JSFH</Equation></Text-field>
</Input>
</Group></Presentation-Block>
</Section>
<Section collapsed="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 4" layout="Heading 4">2.3.1.4 Advection Partial Differential Equation</Text-field></Title><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L8729" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JSFH</Equation></Text-field>
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</Group></Presentation-Block><Table interior="group" showinput="true" alignment="left" exterior="all" width="82.1008984105045%" labelreference="L16807" showlabel="true" captionalignment="0" title="" order="row" drawcaption="false" randomized="false" captionposition="1" plotalignlists="" pagebreak="cell" postexecute="insert" showgroup="true"><Table-Column weight="456" separator="true"></Table-Column><Table-Column weight="732" separator="true"></Table-Column><Table-Row align="top" separator="true"><Table-Cell columnspan="2" backgroundstyle="1" rowspan="1" padding="5" fillcolor="[102,102,153]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L21722" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" foreground="[255,255,255]" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStmb3JlZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L21720" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" foreground="[255,255,255]" layout="Normal" alignment="centred"><Font foreground="[255,255,255]">ADVECTION PARTIAL DIFFERENTIAL EQUATIONS</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L21719" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" foreground="[255,255,255]" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStmb3JlZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
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</Group></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell columnspan="2" backgroundstyle="1" rowspan="1" padding="5" fillcolor="[204,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L21721" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
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</Group></Presentation-Block><Presentation-Block><CodeEditor-ExecGroup view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L21718" applyint="true" applyrational="true" display="code"><EC-CodeEditor id="CodeEditRegion3" visible="false" pixel-width="500" pixel-height="200" code-language="text/maple" autoexpand="true" wrapping="false" show-border="true" code-line-numbers="true">#RESTART AND LOAD PACKAGES
restart:
with(PDETools):</EC-CodeEditor></CodeEditor-ExecGroup></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16810" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
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</Group></Presentation-Block></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16811" drawlabel="true" applyint="true" applyrational="true" applyexponent="false" redirect-target="L16814">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
</Input>
<Output>
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<Group view="presentation" hide-input="true" hide-output="false" inline-output="false" labelreference="L16814" drawlabel="true" applyint="true" applyrational="true" applyexponent="false" redirect-source="L16811">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L16811" view="label" executable="true"></Label>); # input placeholder</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LywmLUklZGlmZkclKnByb3RlY3RlZEc2JC1JIlBHNiI2JEkidEdGKkkickdGKkYsIiIiKiZJImNHRipGLi1GJTYkRihGLUYuRi4iIiE=</Equation></Text-field>
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</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16815" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16812" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
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<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16813" drawlabel="true" applyint="true" applyrational="true" applyexponent="false" redirect-target="L16816">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
</Input>
<Output>
<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
</Output>
</Group>
<Group view="presentation" hide-input="true" hide-output="false" inline-output="false" labelreference="L16816" drawlabel="true" applyint="true" applyrational="true" applyexponent="false" redirect-source="L16813">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L16813" view="label" executable="true"></Label>); # input placeholder</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly1JIlBHNiI2JEkidEdGJUkickdGJS1JJF9GMUdGJTYjLCYqJkkiY0dGJSIiIkYnRi8hIiJGKEYv</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16817" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16823" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Here we notice that the solution will be the only one arbitrary function multiplied by a factor <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW9HRiQ2LVEqJnVtaW51czA7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRkMtSSNtaUdGJDYlUSNjdEYnLyUnaXRhbGljR1EldHJ1ZUYnL0YwUSdpdGFsaWNGJy1GLDYtUSIrRidGL0YyRjVGN0Y5RjtGPUY/RkFGRC1GRzYlUSJyRidGSkZNRi8=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW9HRiQ2LVEqJnVtaW51czA7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRkMtSSNtaUdGJDYlUSNjdEYnLyUnaXRhbGljR1EldHJ1ZUYnL0YwUSdpdGFsaWNGJy1GLDYtUSIrRidGL0YyRjVGN0Y5RjtGPUY/RkFGRC1GRzYlUSJyRidGSkZNRi8=</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16822" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">We produce a particular solution and a general solution as follows:</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16820" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16821" drawlabel="true" applyint="true" applyrational="true" applyexponent="false" redirect-target="L16824">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JVEuYWR2ZWN0aW9uX3NvbEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUYsNiVRJXN1YnNGJ0YvRjItSShtZmVuY2VkR0YkNiQtRiM2Ky1GLDYlUSRfRjFGJ0YvRjItRjY2LVEiPUYnRjlGO0Y+RkBGQkZERkZGSEZKRk0tRiw2JVEoJmFscGhhO0YnL0YwRj1GOS1GNjYtUSIsRidGOUY7L0Y/RjFGQEZCRkRGRkZIL0ZLUSYwLjBlbUYnL0ZOUSwwLjMzMzMzMzNlbUYnLUY2Ni1RIn5GJ0Y5RjtGPkZARkJGREZGRkhGX28vRk5GYG9GY28tRiw2JVEpc2ltcGxpZnlGJ0YvRjItRlM2JC1GIzYlLUYsNiVRJmJ1aWxkRidGL0YyLUZTNiQtRiM2JEYrRjlGOUY5RjlGOUY5LUY2Ni1RIjtGJ0Y5RjtGXm9GQEZCRkRGRkZIRl9vRk0vJStleGVjdXRhYmxlR0Y9Rjk=</Equation></Text-field>
</Input>
<Output>
<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
</Output>
</Group>
<Group view="presentation" hide-input="true" hide-output="false" inline-output="false" labelreference="L16824" drawlabel="true" applyint="true" applyrational="true" applyexponent="false" redirect-source="L16821">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L16821" view="label" executable="true"></Label>); # input placeholder</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly1JIlBHNiI2JEkidEdGJUkickdGJS1JJmFscGhhR0YlNiMsJiomSSJjR0YlIiIiRidGLyEiIkYoRi8=</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16825" drawlabel="true" applyint="true" applyrational="true" applyexponent="false" redirect-target="L16826">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYtLUkjbWlHRiQ2JVE2YWR2ZWN0aW9uX2dlbmVyYWxfc29sRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEqJmNvbG9uZXE7RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtRiw2JVEiUEYnRi9GMi1JKG1mZW5jZWRHRiQ2JC1GIzYmLUYsNiVRInRGJ0YvRjItRjY2LVEiLEYnRjlGOy9GP0YxRkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTlEsMC4zMzMzMzMzZW1GJy1GLDYlUSJyRidGL0YyRjlGOS1GNjYtUSI9RidGOUY7Rj5GQEZCRkRGRkZIRkpGTS1GNjYtUSJ+RidGOUY7Rj5GQEZCRkRGRkZIRmhuL0ZORmluLUYsNiVRJXN1YnNGJ0YvRjItRlM2JC1GIzYoLUYsNiVRLmFkdmVjdGlvbl9zb2xGJ0YvRjJGWkZiby1GLDYlUSRpbnRGJ0YvRjItRlM2JC1GIzYvLUYsNiVRIkFGJ0YvRjItRlM2JC1GIzYkLUYsNiVRImtGJ0YvRjJGOUY5LUY2Ni1RJyZzZG90O0YnRjlGO0Y+RkBGQkZERkZGSEZobkZlb0ZPRlJGWkZib0ZecUZfby1GLDYlUSJhRidGL0YyLUY2Ni1RIy4uRidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSwwLjIyMjIyMjJlbUYnRmVvLUYsNiVRImJGJ0YvRjJGOUY5RjlGOS1GNjYtUSI7RidGOUY7RmduRkBGQkZERkZGSEZobkZNLyUrZXhlY3V0YWJsZUdGPUY5">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</Equation></Text-field>
</Input>
<Output>
<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
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</Group>
<Group view="presentation" hide-input="true" hide-output="false" inline-output="false" labelreference="L16826" drawlabel="true" applyint="true" applyrational="true" applyexponent="false" redirect-source="L16825">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L16825" view="label" executable="true"></Label>); # input placeholder</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly1JIlBHNiI2JEkidEdGJUkickdGJS1JJGludEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYkKiYtSSJBR0YlNiNJImtHRiUiIiItSSZhbHBoYUdGJTYjLCYqJkkiY0dGJUY0RidGNCEiIkYoRjRGNC9GMztJImFHRiVJImJHRiU=</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16827" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16829" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal">Once again, we verify that the proposed solution actually solves the partial differential equation.</Text-field>
</Input>
</Group></Presentation-Block></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16833" drawlabel="true" redirect-target="L16832">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
</Input>
<Output>
<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
</Output>
</Group>
<Group view="presentation" hide-input="true" hide-output="false" inline-output="false" labelreference="L16832" drawlabel="true" redirect-source="L16833">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L16833" view="label" executable="true"></Label>); # input placeholder</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">LyIiIUYj</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16831" drawlabel="true" redirect-target="L16834">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
</Input>
<Output>
<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
</Output>
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<Group view="presentation" hide-input="true" hide-output="false" inline-output="false" labelreference="L16834" drawlabel="true" applyint="true" applyrational="true" applyexponent="false" redirect-source="L16831">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L16831" view="label" executable="true"></Label>); # input placeholder</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">IiIh</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16830" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row></Table><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L8739" drawlabel="true" redirect-target="L8736">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JSFH</Equation></Text-field>
</Input>
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</Section><Presentation-Block>
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<Section collapsed="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 3" layout="Heading 3">2.3.2  The Heat Equation</Text-field></Title>
<Section collapsed="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 4" layout="Heading 4">2.3.2.1  The Heat Equation without Boundary Conditions</Text-field></Title><Presentation-Block>
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<Input>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JSFH</Equation></Text-field>
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<Text-field style="Text" foreground="[255,255,255]" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStmb3JlZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
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<Text-field style="Text" foreground="[255,255,255]" layout="Normal" alignment="centred"><Font foreground="[255,255,255]">HEATH EQUATION WITHOUT BOUNDARY CONDITIONS</Font></Text-field>
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<Text-field style="Text" foreground="[255,255,255]" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStmb3JlZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
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<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L21730" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
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<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
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</Group></Presentation-Block><Presentation-Block><CodeEditor-ExecGroup view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L21729" applyint="true" applyrational="true" display="code"><EC-CodeEditor id="CodeEditRegion4" visible="false" pixel-width="500" pixel-height="200" code-language="text/maple" autoexpand="true" wrapping="false" show-border="true" code-line-numbers="true">#RESTART AND LOAD PACKAGES
restart:
with(PDETools):</EC-CodeEditor></CodeEditor-ExecGroup></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
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<Input>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L16841" view="label" executable="true"></Label>); # input placeholder</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LUksUERFU29sU3RydWNHJSpwcm90ZWN0ZWRHNiQvLUkiUEc2IjYkSSJyR0YpSSJ0R0YpKiYtSSRfRjFHRik2I0YrIiIiLUkkX0YyR0YpNiNGLEYxNyM8JC8tSSVkaWZmR0YkNiRGMkYsLCYqKEkmdGhldGFHRilGMSZJI19jRzYkRiRJKF9zeXNsaWJHRik2I0YxRjFGMkYxRjEqJkkmZGVsdGFHRilGMUYyRjEhIiIvLUY5NiQtRjk2JEYuRitGKyomRj5GMUYuRjE=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly1JIlBHNiI2JEkickdGJUkidEdGJSwmKixJJF9DM0dGJSIiIi1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjKihGKEYsSSZ0aGV0YUdGJUYsJkkjX2NHRi82I0YsRixGLC1GLjYjKiZJJmRlbHRhR0YlRixGKEYsISIiSSRfQzFHRiVGLC1GLjYjKiYpRjUjRiwiIiNGLEYnRixGLEYsKixGK0YsRi1GLEY4RjxJJF9DMkdGJUYsRj5GPEYs</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16853" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">JSFH</Equation></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16842" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16843" drawlabel="true" applyint="true" applyrational="true" applyexponent="false" redirect-target="L16854">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
</Input>
<Output>
<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
</Output>
</Group>
<Group view="presentation" hide-input="true" hide-output="false" inline-output="false" labelreference="L16854" drawlabel="true" applyint="true" applyrational="true" applyexponent="false" redirect-source="L16843">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L16843" view="label" executable="true"></Label>); # input placeholder</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly1JIlBHNiI2JEkickdGJUkidEdGJSwmKiwtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2IyomKUkia0dGJSMiIiIiIiNGNUYnRjVGNUkkX0MzR0YlRjUtRiw2IyooRihGNUkmdGhldGFHRiVGNUYzRjVGNUkkX0MxR0YlRjUtRiw2IyomSSZkZWx0YUdGJUY1RihGNSEiIkY1KixGN0Y1RjhGNUkkX0MyR0YlRjVGK0ZBRj1GQUY1</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16855" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">JSFH</Equation></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16847" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JSFH</Equation></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16848" drawlabel="true" applyint="true" applyrational="true" applyexponent="false" redirect-target="L16856">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
</Input>
<Output>
<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
</Output>
</Group>
<Group view="presentation" hide-input="true" hide-output="false" inline-output="false" labelreference="L16856" drawlabel="true" applyint="true" applyrational="true" applyexponent="false" redirect-source="L16848">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L16848" view="label" executable="true"></Label>); # input placeholder</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">IiIh</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16857" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">JSFH</Equation></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row></Table><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L8755" drawlabel="true" redirect-target="L8253">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">JSFH</Equation></Text-field>
</Input>
</Group>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16849" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">JSFH</Equation></Text-field>
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<Text-field style="Heading 4" layout="Heading 4">2.3.2.2  Heat Equation with Boundary conditions</Text-field></Title><Presentation-Block>
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<Text-field style="Text" foreground="[255,255,255]" layout="Normal" alignment="centred"><Font foreground="[255,255,255]">HEATH EQUATION WITH BOUNDARY CONDITIONS</Font></Text-field>
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<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
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</Group></Presentation-Block><Presentation-Block><CodeEditor-ExecGroup view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L21738" applyint="true" applyrational="true" display="code"><EC-CodeEditor id="CodeEditRegion5" visible="false" pixel-width="500" pixel-height="200" code-language="text/maple" autoexpand="true" wrapping="false" show-border="true" code-line-numbers="true">#RESTART AND LOAD PACKAGES
restart:
with(PDETools):</EC-CodeEditor></CodeEditor-ExecGroup></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
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<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JSFH</Equation></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">JSFH</Equation></Text-field>
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<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16863" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JSFH</Equation></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L16864" view="label" executable="true"></Label>); # input placeholder</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly1JIlBHNiI2JEkickdGJUkidEdGJSomLCYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2IyomKSomSSJhR0YlIiIiSSJrR0YlISIiI0Y1IiIjRjVGJ0Y1RjUtRiw2IywmKiRGMkY1RjVGMUY3RjVGNSwmLUYsNiNGPUY1RjVGNUY3</Equation></Text-field>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">JSFH</Equation></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L8252" view="label" executable="true"></Label>); # input placeholder</Text-field>
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<Text-field style="Heading 3" layout="Heading 3">2.3.3  Simplified Price Model</Text-field></Title><Presentation-Block>
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<Text-field style="Heading 4" layout="Heading 4"><Font bold="true" encoding="UTF-8">2.3.3.1 Bond Price Model with \316\272 small</Font></Text-field></Title><Presentation-Block>
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<Text-field style="Text" foreground="[255,255,255]" layout="Normal" alignment="centred"><Font encoding="UTF-8" foreground="[255,255,255]">BOND PRICE WITH \316\272 SMALL</Font></Text-field>
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</Group></Presentation-Block><Presentation-Block><CodeEditor-ExecGroup view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L19" applyint="true" applyrational="true" display="code"><EC-CodeEditor id="CodeEditRegion6" visible="false" pixel-width="500" pixel-height="200" code-language="text/maple" autoexpand="true" wrapping="false" show-border="true" code-line-numbers="true">#RESTART AND LOAD PACKAGES
restart:
with(PDETools):
with(plots):
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<Text-field style="Text" layout="Normal"><Font bold="true" italic="true">Step 1. Definition and Structure of the Solution</Font></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">JSFH</Equation></Text-field>
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</Group></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16885" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" italic="true" bold="true" layout="Normal"><Font bold="true" italic="true">Step 2. Display the solution</Font></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16886" drawlabel="true" applyint="true" applyrational="true" applyexponent="false" redirect-target="L16890">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
</Input>
<Output>
<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
</Output>
</Group>
<Group view="presentation" hide-input="true" hide-output="false" inline-output="false" labelreference="L16890" drawlabel="true" applyint="true" applyrational="true" applyexponent="false" redirect-source="L16886">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L16886" view="label" executable="true"></Label>); # input placeholder</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LUksUERFU29sU3RydWNHJSpwcm90ZWN0ZWRHNiQvLUkiUEc2IjYkSSJ0R0YpSSJyR0YpKiYtSSRfRjFHRik2I0YrIiIiLUkkX0YyR0YpNiNGLEYxNyM8JC8tSSVkaWZmR0YkNiRGLkYrKiYmSSNfY0c2JEYkSShfc3lzbGliR0YpNiNGMUYxRi5GMS8tRjk2JC1GOTYkRjJGLEYsLCYqKEYyRjFJJmdhbW1hR0YkISIiRjxGMUZJKihGLEYxRjJGMUZIRklGMQ==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly1JIlBHNiI2JEkidEdGJUkickdGJSwmKipJJF9DMUdGJSIiIi1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjKiYmSSNfY0dGLzYjRixGLEYnRixGLEkkX0MyR0YlRiwtSSdBaXJ5QWlHRi82IywmKiYpSSZnYW1tYUdGMCNGLCIiJCEiIkY0RixGQSomRj1GQUYoRixGLEYsRiwqKkYrRixGLUYsSSRfQzNHRiVGLC1JJ0FpcnlCaUdGL0Y6RixGLA==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUYjNigtSSNtaUdGJDYlUSJQRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvRjVRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y/LyUpc3RyZXRjaHlHRj8vJSpzeW1tZXRyaWNHRj8vJShsYXJnZW9wR0Y/LyUubW92YWJsZWxpbWl0c0dGPy8lJ2FjY2VudEdGPy8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRk4tSShtZmVuY2VkR0YkNiQtRiM2KC1GLjYlUSJ0RidGMUY0LUY4Ni1RIixGJ0Y7Rj0vRkFGM0ZCRkRGRkZIRkpGTC9GUFEsMC4zMzMzMzMzZW1GJy1GLjYlUSJyRidGMUY0LyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJy8lKXJlYWRvbmx5R0Y/RjtGO0Zcb0Zfb0Y7LUY4Ni1RIj1GJ0Y7Rj1GQEZCRkRGRkZIRkovRk1RLDAuMjc3Nzc3OGVtRicvRlBGZW8tRiM2Ji1GIzYqLUYuNiVRJF9DMUYnRjFGNC1GODYtUTEmSW52aXNpYmxlVGltZXM7RidGO0Y9RkBGQkZERkZGSEZKRkxGTy1JJW1zdXBHRiQ2JS1GODYtUS8mRXhwb25lbnRpYWxFO0YnRjtGPUZARkJGREZGRkhGSkZML0ZQUSwwLjExMTExMTFlbUYnLUYjNiYtRi42JVEnJiM5NDU7RicvRjJGP0Y7Rl5wRlZGOy8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGXnAtRi42JVEkX0MyRidGMUY0Rl5wLUYjNigtRi42JVEnQWlyeUFpRidGXnFGO0Y3LUZSNiQtRiM2Ji1GIzYnLUY4Ni1RKiZ1bWludXMwO0YnRjtGPUZARkJGREZGRkhGSi9GTVEsMC4yMjIyMjIyZW1GJy9GUEZkci1JJm1mcmFjR0YkNigtRiM2JkZbcUZcb0Zfb0Y7LUYjNiYtRmJwNiUtRi42JVEnJiM5NDc7RidGXnFGOy1GIzYoLUkjbW5HRiQ2JFEiMUYnRjstRjg2LVEiL0YnRjtGPUZAL0ZDRjNGREZGRkhGSi9GTVEsMC4xNjY2NjY3ZW1GJy9GUEZddC1GZXM2JFEiM0YnRjtGXG9GX29GO0ZfcUZcb0Zfb0Y7LyUubGluZXRoaWNrbmVzc0dGZ3MvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGZnQvJSliZXZlbGxlZEdGPy1GODYtUSIrRidGO0Y9RkBGQkZERkZGSEZKRmNyRmVyLUZncjYoLUYjNiZGaW5GXG9GX29GO0Zbc0ZidEZkdEZndEZpdEY7RlxvRl9vRjtGO0Zcb0Zfb0Y7RjtGW3UtRiM2KkZbcEZecEZhcEZecC1GLjYlUSRfQzNGJ0YxRjRGXnAtRiM2KC1GLjYlUSdBaXJ5QmlGJ0ZecUY7RjdGanFGXG9GX29GO0Y7RjtGXG9GX29GOw==">Ly1JIlBHNiI2JEkidEdGJUkickdGJSwmKipJJF9DMUdGJSIiIi1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjKiZJJmFscGhhR0YlRixGJ0YsRixJJF9DMkdGJUYsLUknQWlyeUFpR0YvNiMsJiomKUkmZ2FtbWFHRjAjRiwiIiQhIiJGNEYsRj8qJkY7Rj9GKEYsRixGLEYsKipGK0YsRi1GLEkkX0MzR0YlRiwtSSdBaXJ5QmlHRi9GOEYsRiw=</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16891" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">JSFH</Equation></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16892" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal"><Font bold="true" italic="true">Step 2.  Testing the solution</Font></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16893" drawlabel="true" applyint="true" applyrational="true" applyexponent="false" redirect-target="L16894">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
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<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L16893" view="label" executable="true"></Label>); # input placeholder</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">IiIh</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16895" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">JSFH</Equation></Text-field>
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</Group></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell columnspan="2" backgroundstyle="1" rowspan="1" padding="5" fillcolor="[102,102,153]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L21742" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" foreground="[255,255,255]" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStmb3JlZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">JSFH</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L21744" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" foreground="[255,255,255]" layout="Normal" alignment="centred"><Font foreground="[255,255,255]">THE AirAi AND AiriBi FUNCTIONS</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L21745" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" foreground="[255,255,255]" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStmb3JlZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">JSFH</Equation></Text-field>
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</Group></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L21746" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JSFH</Equation></Text-field>
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<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L21789" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" bold="true" layout="Normal" alignment="centred"><Font bold="true">Parameters</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L21748" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" bold="true" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRicvJSVib2xkR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSVib2xkRicvJStmb250d2VpZ2h0R0Y0">JSFH</Equation></Text-field>
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</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L21778" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
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<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L21790" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L21791" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
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<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L21792" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
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</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L21779" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><Font encoding="UTF-8">\316\263</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L21780" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation><EC-Slider id="Slider18" lower-bound="0" upper-bound="100" control-position="40" major-tick-spacing="20" minor-ticks="10" inputenabled="true" visible="true" filled="true" orientation="false" show-labels="true" show-ticks="true" snap-to-ticks="true" continuous-update="false" pixel-width="190" pixel-height="38"><MapleCode action="position-event-handler">use DocumentTools, Finance, plots in 

Do(a[1]=%Slider18):# Gamma
Do(a[2]=%Slider19):# c

f := proc (gamma, r, c) options operator, arrow; AiryAi(gamma^3*(r-c)) end proc:
g := proc (gamma, r, c) options operator, arrow; AiryBi(gamma^3*(r-c)) end proc:


p1:=plot(f(a[1], r, a[2]), r=-0.01..0.999999*a[2],
title=[typeset(&quot;The AiryAi Function for parameter&quot;, &quot;\134n&quot;, \134gamma,&quot; =&quot;,a[1] ,&quot; and c= &quot;,a[2]), 
font=[TIMES, Italic, 12]],
color=grey,
gridlines=true):



p2:=plot(g(a[1], r, a[2]), r=-0.01..0.999999*a[2],
title=[typeset(&quot;The AiryBi Function for parameter&quot;, &quot;\134n&quot;, \134gamma, &quot;=&quot;,a[1] ,&quot; and c= &quot;,a[2]), 
font=[TIMES, Italic, 12]],
color=grey,
gridlines=true):

Do(%Plot17=display(p1)):
Do(%Plot18=display(p2)):

end use; 
</MapleCode></EC-Slider></Text-field>
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</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L21785" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L21793" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L21794" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L21795" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L21786" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred">c</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L21787" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><EC-Slider id="Slider19" lower-bound="0.0" upper-bound="0.1" control-position="0.09" major-tick-spacing="0.02" minor-ticks="0.01" inputenabled="true" visible="true" filled="true" orientation="false" show-labels="true" show-ticks="true" snap-to-ticks="true" continuous-update="false" pixel-width="190" pixel-height="38"><MapleCode action="position-event-handler">use DocumentTools, Finance, plots in 

Do(a[1]=%Slider18):# Gamma
Do(a[2]=%Slider19):# c

f := proc (gamma, r, c) options operator, arrow; AiryAi(gamma^3*(r-c)) end proc:
g := proc (gamma, r, c) options operator, arrow; AiryBi(gamma^3*(r-c)) end proc:


p1:=plot(f(a[1], r, a[2]), r=-0.01..0.999999*a[2],
title=[typeset(&quot;The AiryAi Function for parameter&quot;, &quot;\134n&quot;, \134gamma,&quot; =&quot;,a[1] ,&quot; and c= &quot;,a[2]), 
font=[TIMES, Italic, 12]],
color=grey,
gridlines=true):



p2:=plot(g(a[1], r, a[2]), r=-0.01..0.999999*a[2],
title=[typeset(&quot;The AiryBi Function for parameter&quot;, &quot;\134n&quot;, \134gamma, &quot;=&quot;,a[1] ,&quot; and c= &quot;,a[2]), 
font=[TIMES, Italic, 12]],
color=grey,
gridlines=true):

Do(%Plot17=display(p1)):
Do(%Plot18=display(p2)):

end use; 
</MapleCode></EC-Slider></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L21782" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L21783" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L21784" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L21747" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L21754" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L21755" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
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restart:
with(PDETools):
with(plots):
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<Text-field style="Text" layout="Normal"><Font bold="true" italic="true">Step 1. Definitions and structure of the solution</Font></Text-field>
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<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
</Output>
</Group>
<Group view="presentation" hide-input="true" hide-output="false" inline-output="false" labelreference="L16935" drawlabel="true" applyint="true" applyrational="true" applyexponent="false" redirect-source="L16934">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L16934" view="label" executable="true"></Label>); # input placeholder</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly1JIlBHNiI2JEkidEdGJUkickdGJS1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjLCQqKCMiIiIiIiNGMiwmSSJzR0YlRjJGJyEiIkYyLCgqJkkma2FwcGFHRiVGMkY1RjJGMiomRjlGMkYnRjJGNiomRjNGMkYoRjJGMkYyRjY=</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16936" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">JSFH</Equation></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16940" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal"><Font bold="true" italic="true">Step 2.  Testing the solution</Font></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16941" drawlabel="true" applyint="true" applyrational="true" applyexponent="false" redirect-target="L16942">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
</Input>
<Output>
<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
</Output>
</Group>
<Group view="presentation" hide-input="true" hide-output="false" inline-output="false" labelreference="L16942" drawlabel="true" applyint="true" applyrational="true" applyexponent="false" redirect-source="L16941">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L16941" view="label" executable="true"></Label>); # input placeholder</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NyQiIiFGIw==</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L16943" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">JSFH</Equation></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell columnspan="2" backgroundstyle="1" rowspan="1" padding="5" fillcolor="[102,102,153]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L22963" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" foreground="[255,255,255]" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStmb3JlZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L22964" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" foreground="[255,255,255]" layout="Normal" alignment="centred"><Font foreground="[255,255,255]">SOLUTION OF P FOR DIFFERENT PARAMETERS</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L22962" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" foreground="[255,255,255]" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStmb3JlZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell columnspan="2" backgroundstyle="1" rowspan="1" padding="5" fillcolor="[204,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L22961" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block><CodeEditor-ExecGroup view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L22965" applyint="true" applyrational="true" display="code"><EC-CodeEditor id="CodeEditRegion8" visible="false" pixel-width="500" pixel-height="200" code-language="text/maple" autoexpand="true" wrapping="false" show-border="true" code-line-numbers="true">#RESTART AND LOAD PACKAGES
restart:
with(PDETools):
with(plots):
</EC-CodeEditor></CodeEditor-ExecGroup></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L22959" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L22572" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" size="11" bold="true" layout="Normal" alignment="centred"><Font bold="true" size="11">Parameters</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L22583" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" size="11" bold="true" layout="Normal" alignment="centred"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRicvJSVzaXplR1EjMTFGJy8lJWJvbGRHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjc=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L22584" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" size="11" bold="true" layout="Normal" alignment="centred"><Font bold="true" encoding="UTF-8" size="11">\316\272</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L22574" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" size="11" bold="true" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L22566" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" size="11" bold="true" layout="Normal" alignment="centred"><EC-Slider id="Slider20" lower-bound="0.0" upper-bound="1.0" control-position="0.7" major-tick-spacing="0.2" minor-ticks="0.1" inputenabled="true" visible="true" filled="true" orientation="false" show-labels="true" show-ticks="true" snap-to-ticks="true" continuous-update="false" pixel-width="190" pixel-height="38"><MapleCode action="position-event-handler">use DocumentTools, plots in 

Do(a[1]=%Slider20):
Do(a[2]=%Slider21):
Do(a[3]=%Slider22):

P:=(t,kappa,r,s)-&gt; exp(-(1/2*(s-t))*(kappa*s-kappa*t+2*r)):
p1:=plot(P(t,a[1], a[2], a[3]), 
t=1..a[3],
gridlines=true,
title=[typeset(&quot;Solution for P&quot;, &quot;\134n&quot;, \134kappa,&quot; =&quot;,a[1], &quot; &quot; , &quot;r=&quot;, a[2],&quot; &quot;, &quot;and s= &quot;,a[3]), 
font=[TIMES, Italic, 12]]):

Do(%Plot19=p1)
end use; 
</MapleCode></EC-Slider></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L22575" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" size="11" bold="true" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L22585" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" size="11" bold="true" layout="Normal" alignment="centred"><Font bold="true" size="11">r</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L22586" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" size="11" bold="true" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L22576" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" size="11" bold="true" layout="Normal" alignment="centred"><EC-Slider id="Slider21" lower-bound="0.01" upper-bound="0.1" control-position="0.03" major-tick-spacing="0.02" minor-ticks="0.01" inputenabled="true" visible="true" filled="true" orientation="false" show-labels="true" show-ticks="true" snap-to-ticks="true" continuous-update="false" pixel-width="190" pixel-height="38"><MapleCode action="position-event-handler">use DocumentTools, plots in 

Do(a[1]=%Slider20):
Do(a[2]=%Slider21):
Do(a[3]=%Slider22):

P:=(t,kappa,r,s)-&gt; exp(-(1/2*(s-t))*(kappa*s-kappa*t+2*r)):
p1:=plot(P(t,a[1], a[2], a[3]), 
t=1..a[3],
gridlines=true,
title=[typeset(&quot;Solution for P&quot;, &quot;\134n&quot;, \134kappa,&quot; =&quot;,a[1], &quot; &quot; , &quot;r=&quot;, a[2],&quot; &quot;, &quot;and s= &quot;,a[3]), 
font=[TIMES, Italic, 12]]):

Do(%Plot19=p1)
end use; 
</MapleCode></EC-Slider></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L22594" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" size="11" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L22569" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" size="11" bold="true" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L22593" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" size="11" bold="true" layout="Normal" alignment="centred"><Font bold="true" size="11">s</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L22570" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" size="11" layout="Normal" alignment="centred"><EC-Slider id="Slider22" lower-bound="5.0" upper-bound="10.0" control-position="6.5" major-tick-spacing="1.0" minor-ticks="0.5" inputenabled="true" visible="true" filled="true" orientation="false" show-labels="true" show-ticks="true" snap-to-ticks="true" continuous-update="false" pixel-width="190" pixel-height="38"><MapleCode action="position-event-handler">use DocumentTools, plots in 

Do(a[1]=%Slider20):
Do(a[2]=%Slider21):
Do(a[3]=%Slider22):

P:=(t,kappa,r,s)-&gt; exp(-(1/2*(s-t))*(kappa*s-kappa*t+2*r)):
p1:=plot(P(t,a[1], a[2], a[3]), 
t=1..a[3],
gridlines=true,
title=[typeset(&quot;Solution for P&quot;, &quot;\134n&quot;, \134kappa,&quot; =&quot;,a[1], &quot; &quot; , &quot;r=&quot;, a[2],&quot; &quot;, &quot;and s= &quot;,a[3]), 
font=[TIMES, Italic, 12]]):

Do(%Plot19=p1)
end use; 
</MapleCode></EC-Slider></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L22580" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L22582" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
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restart:
with(PDETools):
with(plots):
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
</Input>
<Output>
<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
</Output>
</Group>
<Group view="presentation" hide-input="true" hide-output="false" inline-output="false" labelreference="L17087" drawlabel="true" applyint="true" applyrational="true" applyexponent="false" redirect-source="L17083">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L17083" view="label" executable="true"></Label>); # input placeholder</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L17088" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">JSFH</Equation></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L17084" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal"><Font bold="true" italic="true">Step 2. Testing the solutions</Font></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L17085" drawlabel="true" applyint="true" applyrational="true" applyexponent="false" redirect-target="L17089">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
</Input>
<Output>
<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
</Output>
</Group>
<Group view="presentation" hide-input="true" hide-output="false" inline-output="false" labelreference="L17089" drawlabel="true" applyint="true" applyrational="true" applyexponent="false" redirect-source="L17085">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L17085" view="label" executable="true"></Label>); # input placeholder</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NyMiIiE=</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L17090" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">JSFH</Equation></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L17091" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal"><Font bold="true" italic="true">Step 3. Understanding the solution</Font></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L17092" drawlabel="true" applyint="true" applyrational="true" applyexponent="false" redirect-target="L17093">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
</Input>
<Output>
<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
</Output>
</Group>
<Group view="presentation" hide-input="true" hide-output="false" inline-output="false" labelreference="L17093" drawlabel="true" applyint="true" applyrational="true" applyexponent="false" redirect-source="L17092">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L17092" view="label" executable="true"></Label>); # input placeholder</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMsJComLCgqKEkjcjBHRiciIiJJInRHRidGLkkmZ2FtbWFHRiVGLiIiIyomSSJyR0YnRi4sKComSSJSR0YnRi5GMEYuIiIlKiZGMEYuRi1GLiEiJSokSSZrYXBwYUdGJ0YxRi4jRi5GMUYuKiZGM0YuRjtGLiEiIkYuRjBGPkY8</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXN1cEc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEvJkV4cG9uZW50aWFsRTtGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMTExMTExMWVtRictSSVtcm93R0YkNictRiw2LVEqJnVtaW51czA7RidGL0YyRjVGN0Y5RjtGPUY/L0ZCUSwwLjIyMjIyMjJlbUYnL0ZFRk4tRkg2KC1JJm1mcmFjR0YkNigtSSNtbkdGJDYkUSIxRidGLy1GVjYkUSIyRidGLy8lLmxpbmV0aGlja25lc3NHRlgvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGam4vJSliZXZlbGxlZEdGNC1GLDYtUTEmSW52aXNpYmxlVGltZXM7RidGL0YyRjVGN0Y5RjtGPUY/RkEvRkVGQy1GUzYoLUZINiYtRkg2KUZKLUZINipGWUZfby1JI21pR0YkNiVRI3IwRicvJSdpdGFsaWNHUSV0cnVlRicvRjBRJ2l0YWxpY0YnRl9vLUZccDYlUSJ0RidGX3BGYnBGX28tRlxwNiVRJyYjOTQ3O0YnL0ZgcEY0Ri9GLy1GLDYtUSIrRidGL0YyRjVGN0Y5RjtGPUY/Rk1GTy1GSDYmLUZccDYlUSJyRidGX3BGYnBGX28tSSZtc3FydEdGJDYjLUZINigtRkg2KC1GVjYkUSI0RidGL0Zfby1GXHA2JVEiUkYnRl9wRmJwRl9vRmdwRi8tRiw2LVEoJm1pbnVzO0YnRi9GMkY1RjdGOUY7Rj1GP0ZNRk8tRkg2KEZqcUZfb0ZncEZfb0ZbcEYvRltxLUZINiQtRiM2JS1GXHA2JVEnJiM5NTQ7RidGanBGL0ZZLyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0YvRi9GL0ZbcS1GSDYmRmBxRl9vRmlyRi9GLy8lK2ZvcmVncm91bmRHUShbMCwwLDBdRicvJSlyZWFkb25seUdGNEYvLUZINiZGZ3BGYXNGZHNGL0ZmbkZobkZbb0Zdb0Zhc0Zkc0YvRmFzRmRzRi9GXHM=">LUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMsJComLCgqKEkjcjBHRiciIiJJInRHRidGLkkmZ2FtbWFHRiVGLiEiIyomSSJyR0YnRi4sKComSSJSR0YnRi5GMEYuIiIlKiZGMEYuRi1GLiEiJSokSSZrYXBwYUdGJyIiI0YuI0YuRjxGLiomRjNGLkY7Ri5GLkYuRjAhIiIjRj9GPA==</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L17094" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">JSFH</Equation></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell columnspan="2" backgroundstyle="1" rowspan="1" padding="5" fillcolor="[102,102,153]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L23173" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" foreground="[255,255,255]" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStmb3JlZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">JSFH</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L23171" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" foreground="[255,255,255]" layout="Normal" alignment="centred"><Font foreground="[255,255,255]">SOLUTION OF P FOR DIFFERENT PARAMETERS</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L23174" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" foreground="[255,255,255]" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStmb3JlZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">JSFH</Equation></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell columnspan="2" backgroundstyle="1" rowspan="1" padding="5" fillcolor="[204,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L23175" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JSFH</Equation><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JSFH</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block><CodeEditor-ExecGroup view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L23177" applyint="true" applyrational="true" display="code"><EC-CodeEditor id="CodeEditRegion10" visible="false" pixel-width="500" pixel-height="200" code-language="text/maple" autoexpand="true" wrapping="false" show-border="true" code-line-numbers="true">#RESTART AND LOAD PACKAGES
restart:
with(PDETools):
with(plots):
</EC-CodeEditor></CodeEditor-ExecGroup></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L23181" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JSFH</Equation></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L23188" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" size="11" bold="true" layout="Normal" alignment="centred"><Font bold="true" size="11">Parameters</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L23183" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" size="11" bold="true" layout="Normal" alignment="centred"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRicvJSVzaXplR1EjMTFGJy8lJWJvbGRHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjc=">JSFH</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L23185" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" size="11" bold="true" layout="Normal" alignment="centred"><Font bold="true" encoding="UTF-8" size="11">\316\272</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L23193" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" size="11" bold="true" layout="Normal" alignment="centred"><EC-Slider id="Slider23" lower-bound="-1.0" upper-bound="1.0" control-position="-0.5" major-tick-spacing="0.5" minor-ticks="0.1" inputenabled="true" visible="true" filled="true" orientation="false" show-labels="true" show-ticks="true" snap-to-ticks="true" continuous-update="false" pixel-width="190" pixel-height="38"><MapleCode action="position-event-handler">use DocumentTools, plots in 

Do(a[1]=%Slider23):# kappa
Do(a[2]=%Slider24):# r
Do(a[3]=%Slider25):# gamma
Do(a[4]=%Slider26): # R
Do(a[5]=%Slider27): # r0
Do(a[6]=GetProperty('RadioButton0', 'value')):

LF:=(kappa, r , gamma, R, r0, t)-&gt;exp((1/2)*(2*r0*t*gamma+r*sqrt(4*R*gamma-4*gamma*r0+kappa^2)-r*kappa)/gamma):
RF:=(kappa, r , gamma, R, r0, t)-&gt;exp(-(1/2)*(-2*r0*t*gamma+r*sqrt(4*R*gamma-4*gamma*r0+kappa^2)+r*kappa)/gamma):
 
p1:=plot(LF(a[1],a[2],a[3],a[4],a[5],t), 
t=1..30,
gridlines=true,
title=[typeset(&quot;Solution for LF&quot;, &quot;\134n&quot;, 
\134kappa,&quot; =&quot;,evalf(a[1],1),&quot; &quot; ,
&quot;r=&quot;,evalf(a[2],1),&quot; &quot; ,
\134gamma,&quot; =&quot;,evalf(a[3],1),&quot; &quot;,
&quot;R=&quot;,evalf(a[4],1),&quot; &quot; ,
&quot;r0=&quot;,evalf(a[5],1),&quot; &quot; ), 
font=[TIMES, Italic, 12]]):


p2:=plot(RF(a[1],a[2],a[3],a[4],a[5],t), 
t=1..30,
gridlines=true,
title=[typeset(&quot;Solution for LF&quot;, &quot;\134n&quot;, 
\134kappa,&quot; =&quot;,evalf(a[1],1),&quot; &quot; ,
&quot;r=&quot;,evalf(a[2],1),&quot; &quot; ,
\134gamma,&quot; =&quot;,evalf(a[3],1),&quot; &quot;,
&quot;R=&quot;,evalf(a[4],1),&quot; &quot; ,
&quot;r0=&quot;,evalf(a[5],1),&quot; &quot; ), 
font=[TIMES, Italic, 12]]):

if a[6]=&quot;true&quot; then
Do(%Plot20=p1):
else
Do(%Plot20=p2):
end if:

end use; 
</MapleCode></EC-Slider></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L23186" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" size="11" bold="true" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L23187" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" size="11" bold="true" layout="Normal" alignment="centred"><Font bold="true" size="11">r</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L23192" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" size="11" bold="true" layout="Normal" alignment="centred"><EC-Slider id="Slider24" lower-bound="0.01" upper-bound="0.1" control-position="0.07" major-tick-spacing="0.02" minor-ticks="0.01" inputenabled="true" visible="true" filled="true" orientation="false" show-labels="true" show-ticks="true" snap-to-ticks="true" continuous-update="false" pixel-width="190" pixel-height="38"><MapleCode action="position-event-handler">use DocumentTools, plots in 

Do(a[1]=%Slider23):# kappa
Do(a[2]=%Slider24):# r
Do(a[3]=%Slider25):# gamma
Do(a[4]=%Slider26): # R
Do(a[5]=%Slider27): # r0
Do(a[6]=GetProperty('RadioButton0', 'value')):

LF:=(kappa, r , gamma, R, r0, t)-&gt;exp((1/2)*(2*r0*t*gamma+r*sqrt(4*R*gamma-4*gamma*r0+kappa^2)-r*kappa)/gamma):
RF:=(kappa, r , gamma, R, r0, t)-&gt;exp(-(1/2)*(-2*r0*t*gamma+r*sqrt(4*R*gamma-4*gamma*r0+kappa^2)+r*kappa)/gamma):
 
p1:=plot(LF(a[1],a[2],a[3],a[4],a[5],t), 
t=1..30,
gridlines=true,
title=[typeset(&quot;Solution for LF&quot;, &quot;\134n&quot;, 
\134kappa,&quot; =&quot;,evalf(a[1],1),&quot; &quot; ,
&quot;r=&quot;,evalf(a[2],1),&quot; &quot; ,
\134gamma,&quot; =&quot;,evalf(a[3],1),&quot; &quot;,
&quot;R=&quot;,evalf(a[4],1),&quot; &quot; ,
&quot;r0=&quot;,evalf(a[5],1),&quot; &quot; ), 
font=[TIMES, Italic, 12]]):


p2:=plot(RF(a[1],a[2],a[3],a[4],a[5],t), 
t=1..30,
gridlines=true,
title=[typeset(&quot;Solution for LF&quot;, &quot;\134n&quot;, 
\134kappa,&quot; =&quot;,evalf(a[1],1),&quot; &quot; ,
&quot;r=&quot;,evalf(a[2],1),&quot; &quot; ,
\134gamma,&quot; =&quot;,evalf(a[3],1),&quot; &quot;,
&quot;R=&quot;,evalf(a[4],1),&quot; &quot; ,
&quot;r0=&quot;,evalf(a[5],1),&quot; &quot; ), 
font=[TIMES, Italic, 12]]):

if a[6]=&quot;true&quot; then
Do(%Plot20=p1):
else
Do(%Plot20=p2):
end if:

end use; </MapleCode></EC-Slider></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L23172" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" size="11" bold="true" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L23176" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" size="11" bold="true" layout="Normal" alignment="centred"><Font bold="true" encoding="UTF-8" size="11">\316\263</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L23178" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" size="11" bold="true" layout="Normal" alignment="centred"><EC-Slider id="Slider25" lower-bound="0.0" upper-bound="1.0" control-position="0.7" major-tick-spacing="0.2" minor-ticks="0.1" inputenabled="true" visible="true" filled="true" orientation="false" show-labels="true" show-ticks="true" snap-to-ticks="true" continuous-update="false" pixel-width="190" pixel-height="38"><MapleCode action="position-event-handler">use DocumentTools, plots in 

Do(a[1]=%Slider23):# kappa
Do(a[2]=%Slider24):# r
Do(a[3]=%Slider25):# gamma
Do(a[4]=%Slider26): # R
Do(a[5]=%Slider27): # r0
Do(a[6]=GetProperty('RadioButton0', 'value')):

LF:=(kappa, r , gamma, R, r0, t)-&gt;exp((1/2)*(2*r0*t*gamma+r*sqrt(4*R*gamma-4*gamma*r0+kappa^2)-r*kappa)/gamma):
RF:=(kappa, r , gamma, R, r0, t)-&gt;exp(-(1/2)*(-2*r0*t*gamma+r*sqrt(4*R*gamma-4*gamma*r0+kappa^2)+r*kappa)/gamma):
 
p1:=plot(LF(a[1],a[2],a[3],a[4],a[5],t), 
t=1..30,
gridlines=true,
title=[typeset(&quot;Solution for LF&quot;, &quot;\134n&quot;, 
\134kappa,&quot; =&quot;,evalf(a[1],1),&quot; &quot; ,
&quot;r=&quot;,evalf(a[2],1),&quot; &quot; ,
\134gamma,&quot; =&quot;,evalf(a[3],1),&quot; &quot;,
&quot;R=&quot;,evalf(a[4],1),&quot; &quot; ,
&quot;r0=&quot;,evalf(a[5],1),&quot; &quot; ), 
font=[TIMES, Italic, 12]]):


p2:=plot(RF(a[1],a[2],a[3],a[4],a[5],t), 
t=1..30,
gridlines=true,
title=[typeset(&quot;Solution for LF&quot;, &quot;\134n&quot;, 
\134kappa,&quot; =&quot;,evalf(a[1],1),&quot; &quot; ,
&quot;r=&quot;,evalf(a[2],1),&quot; &quot; ,
\134gamma,&quot; =&quot;,evalf(a[3],1),&quot; &quot;,
&quot;R=&quot;,evalf(a[4],1),&quot; &quot; ,
&quot;r0=&quot;,evalf(a[5],1),&quot; &quot; ), 
font=[TIMES, Italic, 12]]):

if a[6]=&quot;true&quot; then
Do(%Plot20=p1):
else
Do(%Plot20=p2):
end if:

end use; </MapleCode></EC-Slider></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L23927" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" size="11" bold="true" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L23921" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" size="11" bold="true" layout="Normal" alignment="centred"><Font bold="true" size="11">R</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L23922" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" size="11" bold="true" layout="Normal" alignment="centred"><EC-Slider id="Slider26" lower-bound="0.0" upper-bound="10.0" control-position="1.0" major-tick-spacing="2.0" minor-ticks="1.0" inputenabled="true" visible="true" filled="true" orientation="false" show-labels="true" show-ticks="true" snap-to-ticks="true" continuous-update="false" pixel-width="190" pixel-height="38"><MapleCode action="position-event-handler">use DocumentTools, plots in 

Do(a[1]=%Slider23):# kappa
Do(a[2]=%Slider24):# r
Do(a[3]=%Slider25):# gamma
Do(a[4]=%Slider26): # R
Do(a[5]=%Slider27): # r0
Do(a[6]=GetProperty('RadioButton0', 'value')):

LF:=(kappa, r , gamma, R, r0, t)-&gt;exp((1/2)*(2*r0*t*gamma+r*sqrt(4*R*gamma-4*gamma*r0+kappa^2)-r*kappa)/gamma):
RF:=(kappa, r , gamma, R, r0, t)-&gt;exp(-(1/2)*(-2*r0*t*gamma+r*sqrt(4*R*gamma-4*gamma*r0+kappa^2)+r*kappa)/gamma):
 
p1:=plot(LF(a[1],a[2],a[3],a[4],a[5],t), 
t=1..30,
gridlines=true,
title=[typeset(&quot;Solution for LF&quot;, &quot;\134n&quot;, 
\134kappa,&quot; =&quot;,evalf(a[1],1),&quot; &quot; ,
&quot;r=&quot;,evalf(a[2],1),&quot; &quot; ,
\134gamma,&quot; =&quot;,evalf(a[3],1),&quot; &quot;,
&quot;R=&quot;,evalf(a[4],1),&quot; &quot; ,
&quot;r0=&quot;,evalf(a[5],1),&quot; &quot; ), 
font=[TIMES, Italic, 12]]):


p2:=plot(RF(a[1],a[2],a[3],a[4],a[5],t), 
t=1..30,
gridlines=true,
title=[typeset(&quot;Solution for LF&quot;, &quot;\134n&quot;, 
\134kappa,&quot; =&quot;,evalf(a[1],1),&quot; &quot; ,
&quot;r=&quot;,evalf(a[2],1),&quot; &quot; ,
\134gamma,&quot; =&quot;,evalf(a[3],1),&quot; &quot;,
&quot;R=&quot;,evalf(a[4],1),&quot; &quot; ,
&quot;r0=&quot;,evalf(a[5],1),&quot; &quot; ), 
font=[TIMES, Italic, 12]]):

if a[6]=&quot;true&quot; then
Do(%Plot20=p1):
else
Do(%Plot20=p2):
end if:

end use; 
</MapleCode></EC-Slider></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L23931" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L23924" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" size="11" bold="true" layout="Normal" alignment="centred"><Font bold="true" size="11">r0</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L23925" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" size="11" bold="true" layout="Normal" alignment="centred"><EC-Slider id="Slider27" lower-bound="-0.1" upper-bound="0.1" control-position="-0.030000000000000013" major-tick-spacing="0.04" minor-ticks="0.01" inputenabled="true" visible="true" filled="true" orientation="false" show-labels="true" show-ticks="true" snap-to-ticks="true" continuous-update="false" pixel-width="190" pixel-height="38"><MapleCode action="position-event-handler">use DocumentTools, plots in 

Do(a[1]=%Slider23):# kappa
Do(a[2]=%Slider24):# r
Do(a[3]=%Slider25):# gamma
Do(a[4]=%Slider26): # R
Do(a[5]=%Slider27): # r0
Do(a[6]=GetProperty('RadioButton0', 'value')):

LF:=(kappa, r , gamma, R, r0, t)-&gt;exp((1/2)*(2*r0*t*gamma+r*sqrt(4*R*gamma-4*gamma*r0+kappa^2)-r*kappa)/gamma):
RF:=(kappa, r , gamma, R, r0, t)-&gt;exp(-(1/2)*(-2*r0*t*gamma+r*sqrt(4*R*gamma-4*gamma*r0+kappa^2)+r*kappa)/gamma):
 
p1:=plot(LF(a[1],a[2],a[3],a[4],a[5],t), 
t=1..30,
gridlines=true,
title=[typeset(&quot;Solution for LF&quot;, &quot;\134n&quot;, 
\134kappa,&quot; =&quot;,evalf(a[1],1),&quot; &quot; ,
&quot;r=&quot;,evalf(a[2],1),&quot; &quot; ,
\134gamma,&quot; =&quot;,evalf(a[3],1),&quot; &quot;,
&quot;R=&quot;,evalf(a[4],1),&quot; &quot; ,
&quot;r0=&quot;,evalf(a[5],1),&quot; &quot; ), 
font=[TIMES, Italic, 12]]):


p2:=plot(RF(a[1],a[2],a[3],a[4],a[5],t), 
t=1..30,
gridlines=true,
title=[typeset(&quot;Solution for LF&quot;, &quot;\134n&quot;, 
\134kappa,&quot; =&quot;,evalf(a[1],1),&quot; &quot; ,
&quot;r=&quot;,evalf(a[2],1),&quot; &quot; ,
\134gamma,&quot; =&quot;,evalf(a[3],1),&quot; &quot;,
&quot;R=&quot;,evalf(a[4],1),&quot; &quot; ,
&quot;r0=&quot;,evalf(a[5],1),&quot; &quot; ), 
font=[TIMES, Italic, 12]]):

if a[6]=&quot;true&quot; then
Do(%Plot20=p1):
else
Do(%Plot20=p2):
end if:

end use; 
</MapleCode></EC-Slider></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L23198" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" size="11" bold="true" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L23204" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" size="11" bold="true" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L23205" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" size="11" bold="true" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L23179" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JSFH</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L23194" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation><EC-RadioButton id="RadioButton0" groupname="Group0" caption="Left Function" enabled="true" visible="true" selected="true"><MapleCode action="click-event-handler">use DocumentTools, plots in 

Do(a[1]=%Slider23):# kappa
Do(a[2]=%Slider24):# r
Do(a[3]=%Slider25):# gamma
Do(a[4]=%Slider26): # R
Do(a[5]=%Slider27): # r0
Do(a[6]=GetProperty('RadioButton0', 'value')):

LF:=(kappa, r , gamma, R, r0, t)-&gt;exp((1/2)*(2*r0*t*gamma+r*sqrt(4*R*gamma-4*gamma*r0+kappa^2)-r*kappa)/gamma):
RF:=(kappa, r , gamma, R, r0, t)-&gt;exp(-(1/2)*(-2*r0*t*gamma+r*sqrt(4*R*gamma-4*gamma*r0+kappa^2)+r*kappa)/gamma):
 
p1:=plot(LF(a[1],a[2],a[3],a[4],a[5],t), 
t=1..30,
gridlines=true,
title=[typeset(&quot;Solution for LF&quot;, &quot;\134n&quot;, 
\134kappa,&quot; =&quot;,evalf(a[1],1),&quot; &quot; ,
&quot;r=&quot;,evalf(a[2],1),&quot; &quot; ,
\134gamma,&quot; =&quot;,evalf(a[3],1),&quot; &quot;,
&quot;R=&quot;,evalf(a[4],1),&quot; &quot; ,
&quot;r0=&quot;,evalf(a[5],1),&quot; &quot; ), 
font=[TIMES, Italic, 12]]):


p2:=plot(RF(a[1],a[2],a[3],a[4],a[5],t), 
t=1..30,
gridlines=true,
title=[typeset(&quot;Solution for LF&quot;, &quot;\134n&quot;, 
\134kappa,&quot; =&quot;,evalf(a[1],1),&quot; &quot; ,
&quot;r=&quot;,evalf(a[2],1),&quot; &quot; ,
\134gamma,&quot; =&quot;,evalf(a[3],1),&quot; &quot;,
&quot;R=&quot;,evalf(a[4],1),&quot; &quot; ,
&quot;r0=&quot;,evalf(a[5],1),&quot; &quot; ), 
font=[TIMES, Italic, 12]]):

if a[6]=&quot;true&quot; then
Do(%Plot20=p1):
else
Do(%Plot20=p2):
end if:

end use; 
</MapleCode></EC-RadioButton><EC-RadioButton id="RadioButton1" groupname="Group0" caption="Righ Function" enabled="true" visible="true" selected="false"><MapleCode action="click-event-handler">use DocumentTools, plots in 

Do(a[1]=%Slider23):# kappa
Do(a[2]=%Slider24):# r
Do(a[3]=%Slider25):# gamma
Do(a[4]=%Slider26): # R
Do(a[5]=%Slider27): # r0
Do(a[6]=GetProperty('RadioButton0', 'value')):

LF:=(kappa, r , gamma, R, r0, t)-&gt;exp((1/2)*(2*r0*t*gamma+r*sqrt(4*R*gamma-4*gamma*r0+kappa^2)-r*kappa)/gamma):
RF:=(kappa, r , gamma, R, r0, t)-&gt;exp(-(1/2)*(-2*r0*t*gamma+r*sqrt(4*R*gamma-4*gamma*r0+kappa^2)+r*kappa)/gamma):
 
p1:=plot(LF(a[1],a[2],a[3],a[4],a[5],t), 
t=1..30,
gridlines=true,
title=[typeset(&quot;Solution for LF&quot;, &quot;\134n&quot;, 
\134kappa,&quot; =&quot;,evalf(a[1],1),&quot; &quot; ,
&quot;r=&quot;,evalf(a[2],1),&quot; &quot; ,
\134gamma,&quot; =&quot;,evalf(a[3],1),&quot; &quot;,
&quot;R=&quot;,evalf(a[4],1),&quot; &quot; ,
&quot;r0=&quot;,evalf(a[5],1),&quot; &quot; ), 
font=[TIMES, Italic, 12]]):


p2:=plot(RF(a[1],a[2],a[3],a[4],a[5],t), 
t=1..30,
gridlines=true,
title=[typeset(&quot;Solution for LF&quot;, &quot;\134n&quot;, 
\134kappa,&quot; =&quot;,evalf(a[1],1),&quot; &quot; ,
&quot;r=&quot;,evalf(a[2],1),&quot; &quot; ,
\134gamma,&quot; =&quot;,evalf(a[3],1),&quot; &quot;,
&quot;R=&quot;,evalf(a[4],1),&quot; &quot; ,
&quot;r0=&quot;,evalf(a[5],1),&quot; &quot; ), 
font=[TIMES, Italic, 12]]):

if a[6]=&quot;true&quot; then
Do(%Plot20=p1):
else
Do(%Plot20=p2):
end if:

end use; </MapleCode></EC-RadioButton></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L23195" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L23208" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L23209" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
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<Text-field style="Heading 2" layout="Heading 2">2.4 Vasicek Model: Closed Form Solution</Text-field></Title><Presentation-Block>
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restart:
with(PDETools):
with(plots):
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<Text-field style="Text" italic="true" bold="true" layout="Normal"><Font bold="true" italic="true">Step 1. Bring the solution from the Vasicek original paper (1973).</Font></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">JSFH</Equation></Text-field>
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<Text-field style="Text" italic="true" bold="true" layout="Normal"><Font bold="true" italic="true">Step 2. Test whether it  satisfies the PDE</Font></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
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<Text-field style="Text" foreground="[255,255,255]" layout="Normal" alignment="centred"><Font foreground="[255,255,255]">SOLUTION OF H FOR DIFFERENT PARAMETERS</Font></Text-field>
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<Text-field style="Text" foreground="[255,255,255]" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStmb3JlZ3JvdW5kR1EuWzI1NSwyNTUsMjU1XUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
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<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L25791" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block><CodeEditor-ExecGroup view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L25794" applyint="true" applyrational="true" display="code"><EC-CodeEditor id="CodeEditRegion12" visible="false" pixel-width="500" pixel-height="200" code-language="text/maple" autoexpand="true" wrapping="false" show-border="true" code-line-numbers="true">#RESTART AND LOAD PACKAGES
restart:
with(PDETools):
with(plots):
</EC-CodeEditor></CodeEditor-ExecGroup></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L25796" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L25798" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JSFH</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L25806" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><Font encoding="UTF-8">\317\201</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L25811" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><EC-Slider id="Slider28" lower-bound="0.0" upper-bound="1.0" control-position="0.4" major-tick-spacing="0.2" minor-ticks="0.1" inputenabled="true" visible="true" filled="true" orientation="false" show-labels="true" show-ticks="true" snap-to-ticks="true" continuous-update="false" pixel-width="190" pixel-height="38"><MapleCode action="position-event-handler">use DocumentTools, plots in 
Do(a[1]=%Slider28):# rho
Do(a[2]=%Slider29):# alpha
Do(a[3]=%Slider30):# gamma
Do(a[4]=%Slider31): # s
Do(a[5]=%Slider32): # q

H:=(rho, alpha, gamma, s, q, r,t)-&gt;
exp((1-exp(-alpha*(s-t)))*(gamma+rho*q/alpha-(1/2)*rho^2/alpha^2-r)/
alpha-(s-t)*(gamma+rho*q/alpha-(1/2)*rho^2/alpha^2)-
(1/4)*rho^2*(1-exp(-alpha*(s-t)))^2/alpha^3):

p1:=plot3d(H(a[1],a[2],a[3],a[4],a[5],r,t), r=0.01..0.05, t=1..a[4],
title=&quot;Price of the Bond H(r,t)&quot;,
orientation=[60,60,0],
font=[Times,Roman,10]
):
Do(%Plot21=p1):

end use; 
</MapleCode></EC-Slider></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L25813" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><Font encoding="UTF-8">\316\261</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L25814" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><EC-Slider id="Slider29" lower-bound="0.0" upper-bound="1.0" control-position="0.30000000000000004" major-tick-spacing="0.2" minor-ticks="0.1" inputenabled="true" visible="true" filled="true" orientation="false" show-labels="true" show-ticks="true" snap-to-ticks="true" continuous-update="false" pixel-width="190" pixel-height="38"><MapleCode action="position-event-handler">use DocumentTools, plots in 
Do(a[1]=%Slider28):# rho
Do(a[2]=%Slider29):# alpha
Do(a[3]=%Slider30):# gamma
Do(a[4]=%Slider31): # s
Do(a[5]=%Slider32): # q

H:=(rho, alpha, gamma, s, q, r,t)-&gt;
exp((1-exp(-alpha*(s-t)))*(gamma+rho*q/alpha-(1/2)*rho^2/alpha^2-r)/
alpha-(s-t)*(gamma+rho*q/alpha-(1/2)*rho^2/alpha^2)-
(1/4)*rho^2*(1-exp(-alpha*(s-t)))^2/alpha^3):

p1:=plot3d(H(a[1],a[2],a[3],a[4],a[5],r,t), r=0.01..0.05, t=1..a[4],
title=&quot;Price of the Bond H(r,t)&quot;,
orientation=[60,60,0],
font=[Times,Roman,10]
):
Do(%Plot21=p1):

end use; 
</MapleCode></EC-Slider></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L25816" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><Font encoding="UTF-8">\316\263</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L25817" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><EC-Slider id="Slider30" lower-bound="0.0" upper-bound="1.0" control-position="0.5" major-tick-spacing="0.2" minor-ticks="0.1" inputenabled="true" visible="true" filled="true" orientation="false" show-labels="true" show-ticks="true" snap-to-ticks="true" continuous-update="false" pixel-width="190" pixel-height="38"><MapleCode action="position-event-handler">use DocumentTools, plots in 
Do(a[1]=%Slider28):# rho
Do(a[2]=%Slider29):# alpha
Do(a[3]=%Slider30):# gamma
Do(a[4]=%Slider31): # s
Do(a[5]=%Slider32): # q

H:=(rho, alpha, gamma, s, q, r,t)-&gt;
exp((1-exp(-alpha*(s-t)))*(gamma+rho*q/alpha-(1/2)*rho^2/alpha^2-r)/
alpha-(s-t)*(gamma+rho*q/alpha-(1/2)*rho^2/alpha^2)-
(1/4)*rho^2*(1-exp(-alpha*(s-t)))^2/alpha^3):

p1:=plot3d(H(a[1],a[2],a[3],a[4],a[5],r,t), r=0.01..0.05, t=1..a[4],
title=&quot;Price of the Bond H(r,t)&quot;,
orientation=[60,60,0],
font=[Times,Roman,10]
):
Do(%Plot21=p1):

end use; 
</MapleCode></EC-Slider></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L25819" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred">s</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L25820" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><EC-Slider id="Slider31" lower-bound="0" upper-bound="20" control-position="4" major-tick-spacing="4" minor-ticks="1" inputenabled="true" visible="true" filled="true" orientation="false" show-labels="true" show-ticks="true" snap-to-ticks="true" continuous-update="false" pixel-width="190" pixel-height="38"><MapleCode action="position-event-handler">use DocumentTools, plots in 
Do(a[1]=%Slider28):# rho
Do(a[2]=%Slider29):# alpha
Do(a[3]=%Slider30):# gamma
Do(a[4]=%Slider31): # s
Do(a[5]=%Slider32): # q

H:=(rho, alpha, gamma, s, q, r,t)-&gt;
exp((1-exp(-alpha*(s-t)))*(gamma+rho*q/alpha-(1/2)*rho^2/alpha^2-r)/
alpha-(s-t)*(gamma+rho*q/alpha-(1/2)*rho^2/alpha^2)-
(1/4)*rho^2*(1-exp(-alpha*(s-t)))^2/alpha^3):

p1:=plot3d(H(a[1],a[2],a[3],a[4],a[5],r,t), r=0.01..0.05, t=1..a[4],
title=&quot;Price of the Bond H(r,t)&quot;,
orientation=[60,60,0],
font=[Times,Roman,10]
):
Do(%Plot21=p1):

end use; 
</MapleCode></EC-Slider></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L25830" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred">q</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L25831" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><EC-Slider id="Slider32" lower-bound="-1.0" upper-bound="1.0" control-position="-0.10000000000000014" major-tick-spacing="0.4" minor-ticks="0.1" inputenabled="true" visible="true" filled="true" orientation="false" show-labels="true" show-ticks="true" snap-to-ticks="true" continuous-update="false" pixel-width="190" pixel-height="38"><MapleCode action="position-event-handler">use DocumentTools, plots in 
Do(a[1]=%Slider28):# rho
Do(a[2]=%Slider29):# alpha
Do(a[3]=%Slider30):# gamma
Do(a[4]=%Slider31): # s
Do(a[5]=%Slider32): # q

H:=(rho, alpha, gamma, s, q, r,t)-&gt;
exp((1-exp(-alpha*(s-t)))*(gamma+rho*q/alpha-(1/2)*rho^2/alpha^2-r)/
alpha-(s-t)*(gamma+rho*q/alpha-(1/2)*rho^2/alpha^2)-
(1/4)*rho^2*(1-exp(-alpha*(s-t)))^2/alpha^3):

p1:=plot3d(H(a[1],a[2],a[3],a[4],a[5],r,t), r=0.01..0.05, t=1..a[4],
title=&quot;Price of the Bond H(r,t)&quot;,
orientation=[60,60,0],
font=[Times,Roman,10]
):
Do(%Plot21=p1):

end use; 
</MapleCode></EC-Slider></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L25822" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L25823" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L25836" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JSFH</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L25799" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
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<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
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<Text-field style="Heading 1" layout="Heading 1">3. Numerical Solutions</Text-field></Title>
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<Text-field style="Heading 2" layout="Heading 2">3.1 Cox-Ingersoll-Ross Model </Text-field></Title><Presentation-Block>
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<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">In mathematical finance, the Cox\342\200\223Ingersoll\342\200\223Ross model (or CIR model) describes the evolution of interest rates. It is a type of &quot;one factor model&quot; (short rate model) as it describes interest rate movements as driven by only one source of market risk. The model can be used in the valuation of interest rate derivatives. It was introduced in 1985 by John C. Cox, Jonathan E. Ingersoll and Stephen A. Ross as an extension of the Vasicek model.</Font></Text-field>
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<Text-field style="Text" layout="Normal">The CIR model specifies that the instantaneous interest rate follows the stochastic differential equation, also named the CIR Process:

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<Text-field style="Text" layout="Normal">where <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2JC1JJW1zdWJHRiQ2JS1GLDYlUSJXRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiQtRiw2JVEidEYnRjdGOi9GO1Enbm9ybWFsRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0ZCRitGQg==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2JC1JJW1zdWJHRiQ2JS1GLDYlUSJXRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiQtRiw2JVEidEYnRjdGOi9GO1Enbm9ybWFsRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0ZCRitGQg==</Equation><Font encoding="UTF-8"> is a Wiener process (modelling the random market risk factor) and a , b , and \317\203  are the parameters. The parameter a  corresponds to the speed of adjustment, b  to the mean and \317\203,  to volatility. The drift factor, </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation>, is exactly the same as in the Vasicek model. It ensures mean reversion of the interest rate towards the long run value b, with speed of adjustment governed by the strictly positive parameter a.</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">The standard deviation factor, \317\203</Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2JC1JJm1zcXJ0R0YkNiMtSSVtc3ViR0YkNiUtRiw2JVEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYkLUYsNiVRInRGJ0Y6Rj0vRj5RJ25vcm1hbEYnLyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGRUYrRkU=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2JC1JJm1zcXJ0R0YkNiMtSSVtc3ViR0YkNiUtRiw2JVEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYkLUYsNiVRInRGJ0Y6Rj0vRj5RJ25vcm1hbEYnLyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGRUYrRkU=</Equation>, avoids the possibility of negative interest rates for all positive values of a and b. An interest rate of zero is also precluded if the condition</Text-field>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation>is met. More generally, when the rate is at a low level (close to zero), the standard deviation also becomes very small, which dampens the effect of the random shock on the rate. Consequently, when the rate gets close to zero, its evolution becomes dominated by the drift factor, which pushes the rate upwards (towards equilibrium).</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">This process can be defined as a sum of squared Ornstein\342\200\223Uhlenbeck process. The CIR is an ergodic process, and possesses a stationary distribution. The same process is used in the Heston model to model stochastic volatility.</Font></Text-field>
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<Text-field style="Text" layout="Normal">The distribution of future values of a CIR process can be computed in closed form:
<Equation executable="false" style="2D Math" input-equation="" display="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">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYsLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYmLUYvNiNRIUYnLUYjNiYtRi82JVEidEYnRjJGNS1JI21vR0YkNi1RIitGJy9GNlEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkovJSlzdHJldGNoeUdGSi8lKnN5bW1ldHJpY0dGSi8lKGxhcmdlb3BHRkovJS5tb3ZhYmxlbGltaXRzR0ZKLyUnYWNjZW50R0ZKLyUnbHNwYWNlR1EsMC4yMjIyMjIyZW1GJy8lJ3JzcGFjZUdGWS1GLzYlUSJURidGMkY1RkZGOkZGLyUvc3Vic2NyaXB0c2hpZnRHUSIwRictRkM2LVEiPUYnRkZGSEZLRk1GT0ZRRlNGVS9GWFEsMC4yNzc3Nzc4ZW1GJy9GZW5GYG8tRi82JVEjY1lGJ0YyRjUtRkM2LVExJkludmlzaWJsZVRpbWVzO0YnRkZGSEZLRk1GT0ZRRlNGVS9GWFEmMC4wZW1GJy9GZW5GaW8tSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdGaW8vJSZkZXB0aEdGYHAvJSpsaW5lYnJlYWtHUShuZXdsaW5lRictRkM2LVEifkYnRkZGSEZLRk1GT0ZRRlNGVUZob0Zqby1GLzYlUSJjRidGMkY1RlxvLUkmbWZyYWNHRiQ2KC1GIzYnLUkobWZlbmNlZEdGJDYkLUYjNiYtSSNtbkdGJDYkUSIxRidGRkZCLUklbXN1cEdGJDYlLUYvNiVRJGV4cEYnL0YzRkpGRi1GIzYlLUZDNi1RKiZ1bWludXMwO0YnRkZGSEZLRk1GT0ZRRlNGVUZXRlotRi82JVEjYVRGJ0YyRjVGRi8lMXN1cGVyc2NyaXB0c2hpZnRHRltvRkZGRkZlby1GIzYkLUZdcjYlLUYvNiVRJyYjOTYzO0YnRmJyRkYtRmlxNiRRIjJGJ0ZGRltzRkZGOkZGLUYjNiZGOi1GIzYmLUZpcTYkUSI0RidGRkZlby1GLzYlUSJhRidGMkY1RkZGOkZGLyUubGluZXRoaWNrbmVzc0dGW3IvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGZXQvJSliZXZlbGxlZEdGSkZG</Equation></Text-field>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
<Text-field style="Text" layout="Normal">Y is a non-central Chi-Squared distribution with <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkmbWZyYWNHRiQ2KC1GIzYoLUkjbW5HRiQ2JFEiNEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RJyZzZG90O0YnRjQvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC1JI21pR0YkNiVRImFGJy8lJ2l0YWxpY0dRJXRydWVGJy9GNVEnaXRhbGljRidGNy1GUDYlUSJiRidGU0ZWRjQtRiM2JS1JJW1zdXBHRiQ2JS1GUDYlUScmIzk2MztGJy9GVEY9RjQtRiM2JS1GMTYkUSIyRidGNEZTRlYvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRlNGVi8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGW3AvJSliZXZlbGxlZEdGPUY0">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</Equation>  degrees of freedom and non-centrality parameter  <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation></Text-field>
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<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="left" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Font superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="true" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]">A Note on Binomial Trees</Font></Text-field><Table interior="group" showinput="true" alignment="left" exterior="all" width="84.12274849899933%" labelreference="L18781" showlabel="true" captionalignment="0" title="" order="row" drawcaption="false" randomized="false" captionposition="1" plotalignlists="" pagebreak="cell" postexecute="insert" showgroup="true"><Table-Column weight="1261" separator="true"></Table-Column><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
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<Text-field style="Text" layout="Normal">At each step, it is assumed that the underlying instrument will move up or down by a specific factor (u or d) per step of the tree (where, by definition, <Equation executable="false" style="2D Math" input-equation="" 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executable="false" style="2D Math" input-equation="" display="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">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</Equation> So, if  <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiU0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiU0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=</Equation> is the current price, then in the next period the price will either be  <Equation executable="false" style="2D Math" input-equation="" 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  or <Equation executable="false" style="2D Math" input-equation="" 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<Text-field style="Text" layout="Normal">The up and down factors are calculated using the underlying volatility, <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NjM7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NjM7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy</Equation><Font encoding="UTF-8"> \134sigma, and the time duration of a step, t, measured in years (using the day count convention of the underlying instrument). From the condition that the variance of the log of the price is  </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEnJiM5NjM7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYlLUkjbW5HRiQ2JFEiMkYnRjUvRjNRJXRydWVGJy9GNlEnaXRhbGljRicvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLUYvNiVRInRGJ0Y+RkBGNQ==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEnJiM5NjM7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYlLUkjbW5HRiQ2JFEiMkYnRjUvRjNRJXRydWVGJy9GNlEnaXRhbGljRicvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLUYvNiVRInRGJ0Y+RkBGNQ==</Equation> we have:

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<Text-field style="Text" layout="Normal"> Lets stop for a moment. This is like having two possible moveements. One is up one standard deviation and the other is down one standard deviation.</Text-field>
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<Text-field style="Text" layout="Normal">Each one is weighted by the corresponding probability.</Text-field>
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<Text-field style="Text" layout="Normal">If the distribution is symmetric we get back to the original Cox, Ross, &amp; Rubinstein (CRR) method; there are other techniques for generating the lattice, such as &quot;the equal probabilities&quot; tree. The Trinomial tree is a similar model, allowing for an up, down or stable path.</Text-field>
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<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">The CRR method ensures that the tree is recombinant, i.e. if the underlying asset moves up and then down (u,d), the price will be the same as if it had moved down and then up (d,u) \342\200\224 here the two paths merge or recombine. This property reduces the number of tree nodes, and thus accelerates the computation of the option price.</Font></Text-field>
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<Text-field style="Text" layout="Normal"><Font bold="true">An Example of a Binomial Tree Specification</Font></Text-field>
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<Text-field style="Text" bold="true" layout="Normal" alignment="centred"><Font bold="true">Cox Ingersoll Ross Binomial Tree</Font></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">%;</Text-field>
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<Text-field style="Text" layout="Normal" alignment="centred"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JSFH</Equation></Text-field>
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<Text-field style="Text" layout="Normal" alignment="centred"><EC-Button id="Button0" caption="Plot Binomial Tree" pixel-width="300" pixel-height="200" enabled="true" visible="true" show-border="true" user-size="false"><MapleCode action="click-event-handler">use DocumentTools, Finance, plots in 
module()
Do(M = CoxIngersollRossModel(ZeroCurve(%TextArea1), %Slider0, %Slider1, %Slider4, .1)); 
Do(T= ShortRateTree(M,%Slider2, %Slider3)); 
PL:=TreePlot(T, axes = BOXED, thickness = 1, gridlines = true, 
title = &quot;Cox, Ingersoll and Ross Model&quot;, 
titlefont=[TIMES, Italic, 14],
labels = [&quot;time&quot;, &quot;short rate&quot;], 
labelfont=[TIMES,Italic, 12],
labeldirections = [horizontal, vertical]):

Do(%Plot0=display(PL));



end module:
end use; 
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</Section>
<Section collapsed="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 2" layout="Heading 2">3.2  Vasicek Model </Text-field></Title><Presentation-Block>
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<Text-field style="Text" layout="Normal">The model specifies that the instantaneous interest rate follows the stochastic differential equation:</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2JkYrLUYjNihGKy1GIzYmLUYsNiVRImRGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUTEmSW52aXNpYmxlVGltZXM7RicvRjxRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZGLyUpc3RyZXRjaHlHRkYvJSpzeW1tZXRyaWNHRkYvJShsYXJnZW9wR0ZGLyUubW92YWJsZWxpbWl0c0dGRi8lJ2FjY2VudEdGRi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlUtSSVtc3ViR0YkNiUtRiw2JVEickYnRjhGOy1GIzYkLUYsNiVRInRGJ0Y4RjtGQi8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnRkItRj82LVEiPUYnRkJGREZHRklGS0ZNRk9GUS9GVFEsMC4yNzc3Nzc4ZW1GJy9GV0Zkby1GIzYoRistRiM2KC1GLDYlUSJhRidGOEY7Rj4tSShtZmVuY2VkR0YkNiQtRiM2Ji1GLDYlUSJiRidGOEY7LUY/Ni1RKCZtaW51cztGJ0ZCRkRGR0ZJRktGTUZPRlEvRlRRLDAuMjIyMjIyMmVtRicvRldGaXBGWEZCRkJGPi1GLDYlUSNkdEYnRjhGO0ZCLUY/Ni1RIitGJ0ZCRkRGR0ZJRktGTUZPRlFGaHBGanAtRiM2Ji1GLDYlUScmIzk2MztGJy9GOUZGRkJGPi1GWTYlLUYsNiVRI2RXRidGOEY7RmhuRl1vRkJGK0ZCRitGQkYrRkJGK0ZC">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</Equation></Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal">where  <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2JC1JJW1zdWJHRiQ2JS1GLDYlUSJXRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiQtRiw2JVEidEYnRjdGOi9GO1Enbm9ybWFsRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0ZCRitGQg==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2JC1JJW1zdWJHRiQ2JS1GLDYlUSJXRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiQtRiw2JVEidEYnRjdGOi9GO1Enbm9ybWFsRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0ZCRitGQg==</Equation><Font encoding="UTF-8">   is a Wiener process under the risk neutral framework modelling the random market risk factor, in that it models the continuous inflow of randomness into the system. The standard deviation parameter, \134sigma, determines the volatility of the interest rate and in a way characterizes the amplitude of the instantaneous randomness inflow. The typical parameters b, a and \317\203 , together with the initial condition </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2JC1JJW1zdWJHRiQ2JS1GLDYlUSJyRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiQtSSNtbkdGJDYkUSIwRicvRjtRJ25vcm1hbEYnRkMvJS9zdWJzY3JpcHRzaGlmdEdGQkZDRitGQw==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2JC1JJW1zdWJHRiQ2JS1GLDYlUSJyRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiQtSSNtbkdGJDYkUSIwRicvRjtRJ25vcm1hbEYnRkMvJS9zdWJzY3JpcHRzaGlmdEdGQkZDRitGQw==</Equation>, completely characterize the dynamics, and can be quickly characterized as follows, assuming a to be non-negative:</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal">    <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=</Equation> &quot;long term mean level&quot;. All future trajectories of r will evolve around a mean level b in the long run;</Text-field>
<Text-field style="Text" layout="Normal">    <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=</Equation> &quot;speed of reversion&quot;. a characterizes the velocity at which such trajectories will regroup around b in time;</Text-field>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">    \317\203 &quot;instantaneous volatility&quot;, measures instant by instant the amplitude of randomness entering the system. Higher \134sigma implies more randomness</Font></Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal">The following derived quantity is also of interest,</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal">    <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation></Text-field>
</Input>
</Group>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L19795" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">&quot;long term variance&quot;. All future trajectories of r will regroup around the long term mean with such variance after a long time.</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIn5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTEY5">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIn5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTEY5</Equation> and <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NjM7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NjM7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy</Equation> tend to oppose each other: increasing <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NjM7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NjM7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy</Equation> increases the amount of randomness entering the system, but at the same time increasing a amounts to increasing the speed at which the system will stabilize statistically around the long term mean b with a corridor of variance determined also by <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=</Equation>. This is clear when looking at the long term variance,</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">This model is an Ornstein\342\200\223Uhlenbeck stochastic process.</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L19800" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row></Table><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L19861" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JSFH</Equation></Text-field>
</Input>
</Group></Presentation-Block><Table interior="group" showinput="true" alignment="left" exterior="all" width="84.31771894093686%" labelreference="L19860" showlabel="true" captionalignment="0" title="" order="row" drawcaption="false" randomized="false" captionposition="1" plotalignlists="" pagebreak="cell" postexecute="insert" showgroup="true"><Table-Column weight="593" separator="true"></Table-Column><Table-Column weight="649" separator="true"></Table-Column><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L19863" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><Font bold="true">Parameters of the Vasiceck Model </Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L19881" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" size="10" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJSVzaXplR1EjMTBGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">JSFH</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L19874" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" italic="true" size="10" layout="Normal" alignment="centred"><Font italic="true" size="10">r</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L19871" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" italic="true" size="10" layout="Normal" alignment="centred"><EC-Slider id="Slider9" lower-bound="0.01" upper-bound="0.1" control-position="0.02" major-tick-spacing="0.02" minor-ticks="0.0050" inputenabled="true" visible="true" filled="true" orientation="false" show-labels="true" show-ticks="true" snap-to-ticks="true" continuous-update="false" pixel-width="190" pixel-height="38"><MapleCode action="position-event-handler">use DocumentTools, Finance, plots in 
module()
	
############################################################################################
#CALCULATE THE VASICECK MODEL
Do(model=VasicekModel(%Slider9, %Slider10, %Slider11, %Slider12)); 
Do(r=ShortRateProcess(model)):
Do(tree = ShortRateTree(model, 20, 20)):

############################################################################################
#CALCULATE THE PLOTS
Do(PP=PathPlot(r(t), t = 0 .. 1, timesteps = 50, replications = 20, axes = BOXED, thickness = 1, gridlines = true)):
Do(IP=PathPlot(exp(Int(r(u), u = 0 .. t)), t = 0 .. 1, timesteps = 50, replications = 20, axes = BOXED, 
thickness = 1, gridlines = true)):
Do(TT=TreePlot(tree, gridlines = true, thickness = 3, axes = BOXED)):

############################################################################################
#DISPLAY THE PLOTS
Do(%Plot11=display(PP));
Do(%Plot13=display(IP));
Do(%Plot12=display(TT));

end module:
end use; 
</MapleCode></EC-Slider></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L19882" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" italic="true" size="10" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L19880" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" italic="true" size="10" layout="Normal" alignment="centred"><Font encoding="UTF-8" italic="true" size="10">\316\274</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L19876" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" italic="true" size="10" layout="Normal" alignment="centred"><EC-Slider id="Slider10" lower-bound="0.01" upper-bound="0.1" control-position="0.08" major-tick-spacing="0.02" minor-ticks="0.0050" inputenabled="true" visible="true" filled="true" orientation="false" show-labels="true" show-ticks="true" snap-to-ticks="true" continuous-update="false" pixel-width="190" pixel-height="38"><MapleCode action="position-event-handler">use DocumentTools, Finance, plots in 
module()
	
############################################################################################
#CALCULATE THE VASICECK MODEL
Do(model=VasicekModel(%Slider9, %Slider10, %Slider11, %Slider12)); 
Do(r=ShortRateProcess(model)):
Do(tree = ShortRateTree(model, 20, 20)):

############################################################################################
#CALCULATE THE PLOTS
Do(PP=PathPlot(r(t), t = 0 .. 1, timesteps = 50, replications = 20, axes = BOXED, thickness = 1, gridlines = true)):
Do(IP=PathPlot(exp(Int(r(u), u = 0 .. t)), t = 0 .. 1, timesteps = 50, replications = 20, axes = BOXED, 
thickness = 1, gridlines = true)):
Do(TT=TreePlot(tree, gridlines = true, thickness = 3, axes = BOXED)):

############################################################################################
#DISPLAY THE PLOTS
Do(%Plot11=display(PP));
Do(%Plot13=display(IP));
Do(%Plot12=display(TT));

end module:
end use; 
</MapleCode></EC-Slider></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L19878" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" italic="true" size="10" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L19879" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" italic="true" size="10" layout="Normal" alignment="centred"><Font encoding="UTF-8" italic="true" size="10">\316\270</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L19862" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><EC-Slider id="Slider11" lower-bound="0.0" upper-bound="1.0" control-position="0.1" major-tick-spacing="0.2" minor-ticks="0.1" inputenabled="true" visible="true" filled="true" orientation="false" show-labels="true" show-ticks="true" snap-to-ticks="true" continuous-update="false" pixel-width="190" pixel-height="38"><MapleCode action="position-event-handler">use DocumentTools, Finance, plots in 
module()
	
############################################################################################
#CALCULATE THE VASICECK MODEL
Do(model=VasicekModel(%Slider9, %Slider10, %Slider11, %Slider12)); 
Do(r=ShortRateProcess(model)):
Do(tree = ShortRateTree(model, 20, 20)):

############################################################################################
#CALCULATE THE PLOTS
Do(PP=PathPlot(r(t), t = 0 .. 1, timesteps = 50, replications = 20, axes = BOXED, thickness = 1, gridlines = true)):
Do(IP=PathPlot(exp(Int(r(u), u = 0 .. t)), t = 0 .. 1, timesteps = 50, replications = 20, axes = BOXED, 
thickness = 1, gridlines = true)):
Do(TT=TreePlot(tree, gridlines = true, thickness = 3, axes = BOXED)):

############################################################################################
#DISPLAY THE PLOTS
Do(%Plot11=display(PP));
Do(%Plot13=display(IP));
Do(%Plot12=display(TT));

end module:
end use; 
</MapleCode></EC-Slider></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L19867" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" italic="true" size="10" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L19873" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" italic="true" size="10" layout="Normal" alignment="centred"><Font encoding="UTF-8" italic="true" size="10">\317\203</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L19872" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><EC-Slider id="Slider12" lower-bound="0.01" upper-bound="0.1" control-position="0.05" major-tick-spacing="0.02" minor-ticks="0.0050" inputenabled="true" visible="true" filled="true" orientation="false" show-labels="true" show-ticks="true" snap-to-ticks="true" continuous-update="false" pixel-width="190" pixel-height="38"><MapleCode action="position-event-handler">use DocumentTools, Finance, plots in 
module()
	
############################################################################################
#CALCULATE THE VASICECK MODEL
Do(model=VasicekModel(%Slider9, %Slider10, %Slider11, %Slider12)); 
Do(r=ShortRateProcess(model)):
Do(tree = ShortRateTree(model, 20, 20)):

############################################################################################
#CALCULATE THE PLOTS
Do(PP=PathPlot(r(t), t = 0 .. 1, timesteps = 50, replications = 20, axes = BOXED, thickness = 1, gridlines = true)):
Do(IP=PathPlot(exp(Int(r(u), u = 0 .. t)), t = 0 .. 1, timesteps = 50, replications = 20, axes = BOXED, 
thickness = 1, gridlines = true)):
Do(TT=TreePlot(tree, gridlines = true, thickness = 3, axes = BOXED)):

############################################################################################
#DISPLAY THE PLOTS
Do(%Plot11=display(PP));
Do(%Plot13=display(IP));
Do(%Plot12=display(TT));

end module:
end use; 
</MapleCode></EC-Slider></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L19868" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L19866" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L19875" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><Font bold="true">Short Rate</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L19864" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
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</Section>
</Section>
<Section collapsed="true" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 1" layout="Heading 1">4. The Vasicek Model of Short Rates and Bond Valuation</Text-field></Title>
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<Text-field style="Heading 2" layout="Heading 2">4.1 Implementation: A Word on Maple Notation</Text-field></Title><Presentation-Block>
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<Text-field style="Text" layout="Normal">The documentation on how Maple computes the zero curve or discount curve from a stochastic process is ambiguous with respect to how  to specify the initial conditions and the prevailing interest rate  in bond valuation exercises.</Text-field>
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<Text-field style="Text" layout="Normal">In fact, the Maple command requires a &quot;Short Rate Process&quot; and an initial  &quot;rate&quot;.  The question arises on what rate is this one considering that the Stochastic Process is seeded with a rate already.</Text-field>
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<Text-field style="Text" layout="Normal">One possibility is to think that the rate that is specified in the valuation command overrides the initial rate used in the Short Rate model and that Maple keeps all the remaining parameters of the model definition as they are. In this section we make sure that that is the case.</Text-field>
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<Text-field style="Text" layout="Normal">In consequence, the Vasicek Process gives us a sample of spot rates. From such curve or set of curves we can produce the zero and par curves that can be used in the valuation of the appropriate fixed income securities.</Text-field>
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restart;
with(Finance): 
with(plots): 
with(ArrayTools):
with(LinearAlgebra):
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Font style="Text">1. Take the standard model with an initial condition </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2JC1JJW1zdWJHRiQ2JS1GLDYlUSJyRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiQtSSNtbkdGJDYkUSIwRicvRjtRJ25vcm1hbEYnRkMvJS9zdWJzY3JpcHRzaGlmdEdGQkZDRitGQw==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2JC1JJW1zdWJHRiQ2JS1GLDYlUSJyRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiQtSSNtbkdGJDYkUSIwRicvRjtRJ25vcm1hbEYnRkMvJS9zdWJzY3JpcHRzaGlmdEdGQkZDRitGQw==</Equation><Font style="Text"> equal to 0.03.
2. The model generates a random sequence.</Font></Text-field>
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<Text-field style="Text" layout="Normal">3. We take the first replication.</Text-field>
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<Text-field style="Text" layout="Normal">4. We take the first replication to parametrize the <Font italic="true">DiscountBondPrice</Font> command.</Text-field>
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<Text-field style="Text" layout="Normal">5. We compare the first node of the zero curve with the seeded value resulting from the first replication.</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
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<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L19910" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal">6. We display the result in the following plot.</Text-field>
</Input>
</Group></Presentation-Block></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L19911" drawlabel="true" applyint="true" applyrational="true" applyexponent="false" redirect-target="L19912">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYuLUkjbWlHRiQ2JVEjRzFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSomY29sb25lcTtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSpwb2ludHBsb3RGJ0YvRjItSShtZmVuY2VkR0YkNiQtRiM2SC1GUzYmLUYjNiUtRiw2JVEkc2VxRidGL0YyLUZTNiQtRiM2LC1GLDYlUSJBRidGL0YyLUZTNiYtRiM2JC1GLDYlUSJqRidGL0YyRjlGOS8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJy1GUzYmLUYjNiYtSSNtbkdGJDYkUSIxRidGOS1GNjYtUSMuLkYnRjlGO0Y+RkBGQkZERkZGSC9GS1EsMC4yMjIyMjIyZW1GJy9GTlEmMC4wZW1GJy1GYXA2JFEiMkYnRjlGOUY5RmZvRmlvLUY2Ni1RIixGJ0Y5RjsvRj9GMUZARkJGREZGRkgvRktGanAvRk5RLDAuMzMzMzMzM2VtRidGY28tRjY2LVEiPUYnRjlGO0Y+RkBGQkZERkZGSEZKRk1GW3FGZHAtRmFwNiRRIjZGJ0Y5RjlGOUY5RjlGZm9GaW9GXnEtRjY2LVEifkYnRjlGO0Y+RkBGQkZERkZGSEZicUZpcC1GLDYlUSpncmlkbGluZXNGJ0YvRjJGZXEtRiw2JUYxRi9GMkZecUZbci1GLDYlUSZ0aXRsZUYnRi9GMkZlcUZbci1JI21zR0YkNiNRS0NvbXBhcmlzb25+b2Z+Rmlyc3R+Tm9kZX5pbn50aGV+WmVyb35DdXJ2ZUYnRl5xRltyLUYsNiVRJWZvbnRGJ0YvRjJGZXEtRlM2Ji1GIzYpLUYsNiVRJlRpbWVzRidGL0YyRl5xRltyLUYsNiVRJ0l0YWxpY0YnRi9GMkZecS1GYXA2JFEjMTJGJ0Y5RjlGOUZmb0Zpb0ZecUZbci1GLDYlUSdsYWJlbHNGJ0YvRjJGZXEtRlM2Ji1GIzYpLUYsNiNRIUYnLUZncjYjUSlNZXRob2R+MUYnRl5xRltyLUZncjYjUSlNZXRob2R+MkYnRmF0RjlGOUZmb0Zpb0ZecUZbci1GLDYlUTBsYWJlbGRpcmVjdGlvbnNGJ0YvRjJGZXEtRlM2Ji1GIzYmLUYsNiVRK2hvcml6b250YWxGJ0YvRjJGXnEtRiw2JVEpdmVydGljYWxGJ0YvRjJGOUY5RmZvRmlvRl5xRltyLUYsNiVRJmNvbG9yRidGL0YyRmVxLUYsNiVRJWJsdWVGJ0YvRjJGXnFGW3ItRiw2JVErc3ltYm9sc2l6ZUYnRi9GMkZlcS1GYXA2JFEjMjVGJ0Y5RjlGOS1GNjYtUSI6RidGOUY7Rj5GQEZCRkRGRkZIRkpGTS1JJ21zcGFjZUdGJDYmLyUnaGVpZ2h0R1EmMC4wZXhGJy8lJndpZHRoR0ZqcC8lJmRlcHRoR0Zbdy8lKmxpbmVicmVha0dRKG5ld2xpbmVGJ0Zbci1GLDYlUShkaXNwbGF5RidGL0YyLUZTNiQtRiM2JUYrLyUrZXhlY3V0YWJsZUdGPUY5RjktRjY2LVEiO0YnRjlGO0ZhcUZARkJGREZGRkhGYnFGTUZqd0Y5</Equation></Text-field>
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<Output>
<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
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<Group view="presentation" hide-input="true" hide-output="false" inline-output="false" labelreference="L19912" drawlabel="true" applyint="true" applyrational="true" applyexponent="false" redirect-source="L19911">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">%;</Text-field>
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<Text-field style="Text" layout="Normal">7. Another way to test this is by generating an entirely new stochastic process with the initial conditions generated by the previous stochastic process. We plot the results to see if they match, which is the cases.</Text-field>
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<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L26313" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JSFH</Equation><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JSFH</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block><CodeEditor-ExecGroup view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L26309" applyint="true" applyrational="true" display="code"><EC-CodeEditor id="CodeEditRegion14" visible="false" pixel-width="680" pixel-height="200" code-language="text/maple" autoexpand="true" wrapping="false" show-border="true" code-line-numbers="true">#RESTART AND LOAD PACKAGES
restart;
with(Finance): 
with(plots): 
with(ArrayTools):
with(LinearAlgebra):
</EC-CodeEditor></CodeEditor-ExecGroup></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L26312" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JSFH</Equation></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L20123" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><Font bold="true">Parameters of the Vasiceck Model </Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L20141" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" size="10" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJSVzaXplR1EjMTBGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L20134" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" italic="true" size="10" layout="Normal" alignment="centred"><Font italic="true" size="10">r</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L20130" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" italic="true" size="10" layout="Normal" alignment="centred"><EC-Slider id="Slider13" lower-bound="0.01" upper-bound="0.1" control-position="0.015" major-tick-spacing="0.02" minor-ticks="0.0050" inputenabled="true" visible="true" filled="true" orientation="false" show-labels="true" show-ticks="true" snap-to-ticks="true" continuous-update="false" pixel-width="190" pixel-height="38"><MapleCode action="position-event-handler">
use DocumentTools, Finance, Statistics, plots in 
module()
	
############################################################################################
#CALCULATE THE VASICECK MODEL
Do(M=VasicekModel(%Slider13, %Slider14, %Slider15, %Slider16)); 
Do(X=ShortRateProcess(M)):
Do(T= [seq(.6*i, i = 0 .. 50)]); 
Do(S= SamplePath(X(t), t = 0 .. 50, timesteps = 50, replications = 20)):
Do(W = SamplePath(exp(Int(X(u), u = 0 .. t)), t = 0 .. 50, timesteps = 50, replications = 10)):


############################################################################################
#CALCULATE THE PLOTS
Do(P=[]):
Do(GG1=PathPlot(S, thickness = 1, axes = BOXED, gridlines = true)):
Do(GG2=PathPlot(W, thickness = 1, axes = BOXED, gridlines = true)):
#Do(P=seq(Statistics[LineChart](DiscountBondPrice(M, S[1, i], T, output = zerorate), i = 1 .. 51))):
Do(P=Statistics[LineChart](DiscountBondPrice(M, max(S[1,3],0), T, output = zerorate),gridlines=true)):
############################################################################################
#DISPLAY THE PLOTS
Do(%Plot14=display(GG1));
Do(%Plot15=display(GG2));
Do(%Plot16=display(P));

end module:
end use; 
</MapleCode></EC-Slider></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L20144" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" italic="true" size="10" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L20142" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" italic="true" size="10" layout="Normal" alignment="centred"><Font encoding="UTF-8" italic="true" size="10">\316\274</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L20137" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" italic="true" size="10" layout="Normal" alignment="centred"><EC-Slider id="Slider14" lower-bound="0.01" upper-bound="0.1" control-position="0.05999999999999999" major-tick-spacing="0.02" minor-ticks="0.0050" inputenabled="true" visible="true" filled="true" orientation="false" show-labels="true" show-ticks="true" snap-to-ticks="true" continuous-update="false" pixel-width="190" pixel-height="38"><MapleCode action="position-event-handler">
use DocumentTools, Finance, Statistics, plots in 
module()
	
############################################################################################
#CALCULATE THE VASICECK MODEL
Do(M=VasicekModel(%Slider13, %Slider14, %Slider15, %Slider16)); 
Do(X=ShortRateProcess(M)):
Do(T= [seq(.6*i, i = 0 .. 50)]); 
Do(S= SamplePath(X(t), t = 0 .. 50, timesteps = 50, replications = 20)):
Do(W = SamplePath(exp(Int(X(u), u = 0 .. t)), t = 0 .. 50, timesteps = 50, replications = 10)):


############################################################################################
#CALCULATE THE PLOTS
Do(P=[]):
Do(GG1=PathPlot(S, thickness = 1, axes = BOXED, gridlines = true)):
Do(GG2=PathPlot(W, thickness = 1, axes = BOXED, gridlines = true)):
#Do(P=seq(Statistics[LineChart](DiscountBondPrice(M, S[1, i], T, output = zerorate), i = 1 .. 51))):
Do(P=Statistics[LineChart](DiscountBondPrice(M, max(S[1,3],0), T, output = zerorate),gridlines=true)):
############################################################################################
#DISPLAY THE PLOTS
Do(%Plot14=display(GG1));
Do(%Plot15=display(GG2));
Do(%Plot16=display(P));

end module:
end use; 
</MapleCode></EC-Slider></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L20139" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" italic="true" size="10" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L20140" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" italic="true" size="10" layout="Normal" alignment="centred"><Font encoding="UTF-8" italic="true" size="10">\316\270</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L20122" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><EC-Slider id="Slider15" lower-bound="0.0" upper-bound="1.0" control-position="0.1" major-tick-spacing="0.2" minor-ticks="0.1" inputenabled="true" visible="true" filled="true" orientation="false" show-labels="true" show-ticks="true" snap-to-ticks="true" continuous-update="false" pixel-width="190" pixel-height="38"><MapleCode action="position-event-handler">
use DocumentTools, Finance, Statistics, plots in 
module()
	
############################################################################################
#CALCULATE THE VASICECK MODEL
Do(M=VasicekModel(%Slider13, %Slider14, %Slider15, %Slider16)); 
Do(X=ShortRateProcess(M)):
Do(T= [seq(.6*i, i = 0 .. 50)]); 
Do(S= SamplePath(X(t), t = 0 .. 50, timesteps = 50, replications = 20)):
Do(W = SamplePath(exp(Int(X(u), u = 0 .. t)), t = 0 .. 50, timesteps = 50, replications = 10)):


############################################################################################
#CALCULATE THE PLOTS
Do(P=[]):
Do(GG1=PathPlot(S, thickness = 1, axes = BOXED, gridlines = true)):
Do(GG2=PathPlot(W, thickness = 1, axes = BOXED, gridlines = true)):
#Do(P=seq(Statistics[LineChart](DiscountBondPrice(M, S[1, i], T, output = zerorate), i = 1 .. 51))):
Do(P=Statistics[LineChart](DiscountBondPrice(M, max(S[1,3],0), T, output = zerorate),gridlines=true)):
############################################################################################
#DISPLAY THE PLOTS
Do(%Plot14=display(GG1));
Do(%Plot15=display(GG2));
Do(%Plot16=display(P));

end module:
end use; 
</MapleCode></EC-Slider></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L20128" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" italic="true" size="10" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L20133" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" italic="true" size="10" layout="Normal" alignment="centred"><Font encoding="UTF-8" italic="true" size="10">\317\203</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L20129" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><EC-Slider id="Slider16" lower-bound="0.01" upper-bound="0.1" control-position="0.04" major-tick-spacing="0.02" minor-ticks="0.0050" inputenabled="true" visible="true" filled="true" orientation="false" show-labels="true" show-ticks="true" snap-to-ticks="true" continuous-update="false" pixel-width="190" pixel-height="38"><MapleCode action="position-event-handler">
use DocumentTools, Finance, Statistics, plots in 
module()
	
############################################################################################
#CALCULATE THE VASICECK MODEL
Do(M=VasicekModel(%Slider13, %Slider14, %Slider15, %Slider16)); 
Do(X=ShortRateProcess(M)):
Do(T= [seq(.6*i, i = 0 .. 50)]); 
Do(S= SamplePath(X(t), t = 0 .. 50, timesteps = 50, replications = 20)):
Do(W = SamplePath(exp(Int(X(u), u = 0 .. t)), t = 0 .. 50, timesteps = 50, replications = 10)):


############################################################################################
#CALCULATE THE PLOTS
Do(P=[]):
Do(GG1=PathPlot(S, thickness = 1, axes = BOXED, gridlines = true)):
Do(GG2=PathPlot(W, thickness = 1, axes = BOXED, gridlines = true)):
#Do(P=seq(Statistics[LineChart](DiscountBondPrice(M, S[1, i], T, output = zerorate), i = 1 .. 51))):
Do(P=Statistics[LineChart](DiscountBondPrice(M, max(S[1,3],0), T, output = zerorate),gridlines=true)):
############################################################################################
#DISPLAY THE PLOTS
Do(%Plot14=display(GG1));
Do(%Plot15=display(GG2));
Do(%Plot16=display(P));

end module:
end use; 
</MapleCode></EC-Slider></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L20124" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L20126" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" padding="5" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L20136" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><Font bold="true">Short Rate</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L20120" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
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legendvisibility="true">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</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L20621" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><Font italic="true" size="10">Simulation Sequence Number</Font></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L20622" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><EC-Slider id="Slider17" lower-bound="1" upper-bound="51" control-position="46" major-tick-spacing="10" minor-ticks="1" inputenabled="true" visible="true" filled="true" orientation="false" show-labels="true" show-ticks="true" snap-to-ticks="true" continuous-update="false" pixel-width="190" pixel-height="38"><MapleCode action="position-event-handler">
use DocumentTools, Finance, Statistics, plots in 
module()
	
############################################################################################
#CALCULATE THE VASICECK MODEL
Do(M=VasicekModel(%Slider13, %Slider14, %Slider15, %Slider16)); 
Do(X=ShortRateProcess(M)):
Do(T= [seq(.6*i, i = 0 .. 50)]); 
Do(S= SamplePath(X(t), t = 0 .. 50, timesteps = 50, replications = 20)):
Do(W = SamplePath(exp(Int(X(u), u = 0 .. t)), t = 0 .. 50, timesteps = 50, replications = 10)):


############################################################################################
#CALCULATE THE PLOTS
Do(P=[]):
Do(GG1=PathPlot(S, thickness = 1, axes = BOXED, gridlines = true)):
Do(GG2=PathPlot(W, thickness = 1, axes = BOXED, gridlines = true)):
#Do(P=seq(Statistics[LineChart](DiscountBondPrice(M, S[1, i], T, output = zerorate), i = 1 .. 51))):
Do(P=Statistics[LineChart](DiscountBondPrice(M, max(S[1,3],0), T, output = zerorate),gridlines=true)):
############################################################################################
#DISPLAY THE PLOTS
Do(%Plot14=display(GG1));
Do(%Plot15=display(GG2));
Do(%Plot16=display(P));

end module:
end use; 
 </MapleCode></EC-Slider></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row></Table><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L20035" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
</Input>
</Group></Presentation-Block>
</Section>
</Section><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L21687" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L57" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JSFH</Equation></Text-field>
</Input>
</Group></Presentation-Block>
</Worksheet>